Platform?
Windows

Which controllers specifically did you try?
Dualshock 4, both on Bluetooth and wired
Logitech F310, wired.

When using wired method, did you disable any bluetooth options to avoid interference?
Yes.

Do you have multiple controllers or other 3rd party devices hooked up the machine?
Just a USB mouse.

Did anything change in the computer's environment that may have contributed to the problem?
Brand new laptop, less than 2 months old. This controller disconnection issue occurred Day 1 of me trying the controller on PC.

Try running a clean boot on the machine to see if that may help (disable any programs that may be interfering with the game such as discord if applicable)
Tried, still happens.

Wired or wireless connection:
Wired

Internet Service Provider:
AT&T.