@BelDare  As a general bit of advice, when asking about specific technical problem scenarios like this, it helps to provide specific technical information.  In this case, the exact external NVMe storage device model (or enclosure model) would be useful.  The specific laptop model would be useful, since "G5" refers to an entire product line that includes multiple models introduced over a few years, so saying "G5" is a bit like saying you have a BMW 3 Series.  But offhand I'd suggest updating your system's BIOS and (if applicable) its Thunderbolt 3 controller firmware.

Thank you @jphughan !

I am really sorry for not providing the info, I thought that perhaps this was something simple and I didn't want to bother anyone with a bunch of details.
The storage was bought in two parts; the enclosure is an asus rog strix arion and I fitted inside a 2TB nvme adata drive.
The PC is a dell G5 5590 sold in Brazil, bearing an i7 CPU and geforce RTX2060. It has three USB ports, a type-c and two type-a 3.0.
I've tried the storage on all ports and got the same behavior.

As for your suggestion, I updated the BIOS as one of the fixes that I found over the internet and it didn't solve the issue.

@BelDare  Hmm, very strange then.  I was going to suggest different cables in case something about that system caused it to be more sensitive to a cable issue than some other PCs where the same cable worked fine, but it sounds like you've done that and have even tried connecting it to USB-A ports.  If the USB-C and USB-A ports both behave the same way, then I'm wondering if this is a software-level conflict, possibly with some driver you've got installed on that system and not elsewhere.  One way to test that would be to boot your G5 into a Windows PE/RE environment, which is essentially a "mini" version of Windows that would support USB 3.0 and external storage, but wouldn't have all the extra drivers and applications of your full Windows environment.  If it worked properly there, then it would be something within your Windows environment.  If not, then it would suggest a hardware/firmware issue.  There are various applications that use Windows PE/RE for things.  One that I use is Macrium Reflect, which is a popular disk imaging and cloning application.  It can create bootable "Rescue Media" that runs on Windows PE/RE, so you could boot your system into that and see if your disk maintains a stable connection there.  You could even run a benchmark tool in there to generate some load.  CrystalDiskMark is a popular choice and runs fine on Windows PE/RE.  Just get the portable version of the app so you don't have to run an installer.

I think you need the dell docking station which works like an external closure box which can power and display pictures on displays while also giving you external storage.

https://www.dell.com/en-us/work/shop/dell-dock-wd19-90w-power-delivery-130w-ac/apd/210-ARIO/pc-accessories

@sprinteroz Windows 8 and newer have native support for USB 3.x, so unless the system has some USB host controller chipset that doesn't rely on native support, you shouldn't need ot update USB drivers.  ASMedia's controller requires its own drivers, and that has caused it to have various problems where it's been implemented, such as on Dell's TB16 docking station.  Dell's replacement docking station for that model is the WD19TB, and it switched to an Intel controller that doesn't require that separate driver.

Sounds like a driver issue, try this program driver booster it will find out if your usb drives are out of date and will find other out of date drivers you may need. 

Also have you tried to hook it up through a usb hub to see if it connects that way?

That’s informative!

@BelDare  Interesting finding, but I don’t really see how the RST driver would be involved since the RST controller isn’t used for USB storage. If you had a TB3 enclosure, then MAYBE it would be involved since at that point it would be directly on PCIe like an internal NVMe SSD, but even then I’m not sure. But if you want to investigate whether RST might be causing a problem even for drives it doesn’t directly manage, first try updating the RST driver directly from Intel. If you want to eliminate RST entirely, you can do that as long as you’re not actually using RAID or an Intel Optane device. To do that, go into your BIOS and switch your system from RAID to AHCI mode. You’ll see a warning that this should only be done before an OS install. Ignore that, but you will then need to boot your system into Safe Mode once in order for Windows to adjust its normal boot-time driver load configuration to switch from RST to the native Windows AHCI/NVMe driver. After just allowing Windows to load in Safe Mode, reboot and you should be able to start normally.

hello @jphughan, sorry for the late response!
Since you sugested troubleshooting steps I hadn't tried, I had to take the time to actually test them.
Booting into safe mode does not disconnect the storage on device manager, but I am unable to mount it on disk management. It also does not mount automatically.
Ingrigued by the behavior, I did some digging and messed with some configurations, narrowing the options down to Intel's rapid storage technology. I was able to reproduce the safe mode behavior on a normal windows session by enabling "prevent sleep mode" on the BIOS, which disables RST.
I'm guessing that either the enclosure, or the NVME drive gives an abnormal response to RST when it tries to put the storage in low energy mode, thus making windows unmount the device and flag it as unreconizable. 
I have no idea on how to test this further or explore this better. Do you have any ideas?
In any case, since the PC was showing critical alerts for the fans and the wi-fi hardware kept disappearing, Dell decided to replace the machine. I'm waiting for the new one to arrive and will test the enclosure on it, but I'll be surpirsed if it actually works. I believe that this setup will not work on any Dell machine that has RST.

Thank you so much for your help, you put me on the right track!

@jphughan The first thing I tried was installing the latest RST version available on Dell's support page. It didn't solve the issue. It also installed an app, though, that is called intel optane memory and storage manager. Even though it shows that my system is not optane ready, I admit I am quite afraid of changing this on the BIOS, since I'll be returning this unit in less than one week.
What put me on this RST / power management track was this error on event viewer:
"Reset to device, \Device\RaidPortX, was issued.", where X increments everytime the storage is disconnected from windows.
Why would windows mount an external storage as a raid drive? It makes no sense at all!

@BelDare  Dell’s drivers aren’t always as new as what’s available from the component vendor, hence my recommendation to go to Intel. Not sure why you’re so worried about changing a BIOS setting given that you can change it back, and especially if you’ll be returning it anyway. If you know how to boot in Safe Mode, you’re perfectly fine. But you can make an image backup of your entire system beforehand if it makes you feel better. Or you can wait for the new system and try this change on that system if you encounter the same problem.

That log entry finding is interesting. Being mounted through a RAID port just means a port that is running through a RAID controller, not necessarily a RAID virtual disk. You can run non-RAIDed disks through a RAID controller, and if your system is in RAID mode, that’s exactly what you’re doing with your internal drive right now. Still, that does at least suggest that your NVMe SSD might actually be routing through the RST controller, which surprises me. Unless the ”RAID port” is something internal to the enclosure.

Why would windows mount an external storage as a raid drive

Because the G5 is marketed a gaming laptop. RAID can improve performance and is popular for gamers to utilize so it could be a default BIOS setting on the G5 that isn't commonly default on non-gaming laptops. I don't know if that's the case, just sayin' 

The big Windows 10 update that landed mid July (Windows 10 2004) has a lot of driver conflict issues. Chances are you've run into one of them. I have an internal m.2 nvme secondary drive I had installed and after updating to the Windows 10-2004 release it disappeared and had to be recovered through driver update and a bit of help from Dell support. 

Ouch, that must’ve been a pain in the neck.