The driver's side door speaker on my 14 Impreza seems to work only when it wants to. Today after a couple of seconds of running in park, the dead speaker started working again. Two minutes later it crapped out again. Is there a way to factory reset the (non touchscreen) stock stereo to see if that's the issue? Am I going to have to take the door panel off to check the connection? Is this a common issue?

I haven't worked on one of those, but the most common cause of such problems is bad wiring between the body and the door where it flexes, followed by burnt out speakers.  Does opening and closing the door, or wiggling the bundle of wires to the door, make it go on and off?  Does thwapping the door over the speaker make it go on and off?  Does poking something through the grille and pushing on the speaker cone make it go on and off?  If it's not the door flex wiring or the speaker, then look into the radio itself and the rest of the harness wiring.