Inspiron 13 7000 - Audio keeps descending to 0

I've gone to the drivers page at Dell to see what drivers are available for this machine and the only one available is the Realtek Audio Driver, yet the Intel High Definition Audio keeps popping up in Device Manager, even after uninstalling it.

Hello. Windows contains its own basic (native) audio driver, based on Intel's specifications, called High Definition Audio Device. The laptop's integrated audio won't function without an audio driver, so the purpose of the native driver is to enable basic audio when the vendor's driver has been removed or not installed. (The "vendor" in your case is Realtek, which made the audio chip on the motherboard.) The native driver and the Realtek driver are not supposed to both appear in the Device Manager at the same time, so if that is happening there might be a problem with your Windows. However it probably is not causing the fading issue.

My wife has a Dell Inspiron 13 7000 series and the volume keeps going down to zero without prompting.

There have been a number of complaints posted about that. The solutions that owners came up with are summarized in the Recent Issues FAQ. Look at these sections

Inspiron (13") 53xx & 73xx (exact models unknown)

Inspiron 13" 5368

Hello, My wife has a Dell Inspiron 13 7000 series and the volume keeps going down to zero without prompting. We've re-installed the audio driver several times, which fixes the issue for a short time. Then, after waking up or rebooting, the volume descends to zero again. I've been installing the Realtek Audio driver, which seems to work, but when it installs, there's an "other" driver that shows up in Device Manager called Intel High Definition Audio, which appears to install improperly. I've gone to the drivers page at Dell to see what drivers are available for this machine and the only one available is the Realtek Audio Driver, yet the Intel High Definition Audio keeps popping up in Device Manager, even after uninstalling it.

I have an Inspiron 17 7779 on which I think I have see the sound issue.  But it stopped after some driver updates and, as far as I know, has not done it again.  If there is anyway you can explain how I might try to duplicate the issue on my system, I would give it a try.

When I saw the problem on my system, the Volume level meters which are accessible from the Speaker icon, showed the input volume as normal but the output device volume as almost 0.

The Intel sound driver is for the HDMI output.

Are there any Bios updates for your system?

When I update a driver, I will download a replacement driver, then use Device Manager to uninstall the current one and reboot.  I do this offline so if only the one driver is available, the reboot will install the Windows Basic driver.  If you have other Realtek driver versions on your system it will reinstall that one so you may have to go through the process until you get the Microsoft drivers

Then, while still offline, install the most recent driver you downloaded.

It is very easy to hit the volume switch on the side, if your 15 inch model has one.

The Intel sound driver is for the HDMI output.

If it has Intel integrated graphics i would expect the HDMI audio driver to be named "Intel display Audio".

your 15 inch model

It's a "Dell Inspiron 13 7000 series". Those 13" 7000's seem to be particularly prone to the fading issue.