Check your under hood wiring connections near the passenger side battery. Pull apart the main engine wiring harness connector (near the dipstick) and check/clean/grease the pins there. Then work your way back to the battery and inspect all the quick connects along the way, and fusible links. My 1986 will be a little different, but I was able to find a partially melted quick connect that was corroded internally, causing the plastic casing to melt (was warm to the touch when I found it). it was located near the starter relay on the inner passenger side fender.
In my case, I wasn't loosing the clock settings. Instead the truck's power would flicker when performing a lane change and using the blinker. I ended up cutting the quick connect out completely and soldering the wires under water tight heat shrink. Never had a problem in the years since.
Having said that, the radio should have its own internal smoothing capacitors, which are most likely electrolytic style...they also don't like work in the cold...