Same problem here: active pen 557 on Dell 7285, Win 10 looses connection way too often. Batteries are all new!
I speak about the writing functionality, not the button at the back. Therefore, i guess it's NOT a bluetooth problem. Bluetooth is run by 2x 319 batteries, yet writing is powered by the AAAA battery.
As all others report here very frequently, the writing functionality drops randomly. After removing AAAA battery or even dropping the pen (as others wrote) the functionality is back - but only randomly.
Therefore, DELL, this makes the tablet/writing mode completely useless as it does not work reliably!
Thanks for the idea to troubleshoot the batteries. I seemed to have fixed mine by wrapping the retainer clip with tape. This ensures that the batteries stay in contact with each other and that the retainer clip is tight within the cylinder. I've tried to shake it loose but this seems to have solved the problem.
For anyone having issues with this specific pen. I was in the same situation as you until I installed the drivers for the pen: https://www.dell.com/support/home/uk/en/ukdhs1/product-support/product/dell-active-pen-pn557w/driver...
Since then, I never had a drop in connection. The pen worked flawlessly whenever I wanted to use it.
I have installed the latest driver on my dell 5300 2-in-1 from here but still pen looses connection from time to time (top button won't work): https://www.dell.com/support/home/uk/en/ukdhs1/product-support/product/dell-active-pen-pn557w/driver...
When I go to the bluetooth driver and I select checking for the latest version of the driver, windows says it's already up-to-date. I have the pn577w.
Any further ideas?