A machine at this age having a thousand solder point could easily have "cold" cracked solder some where. It could show up as a heat related problem as warming the system a bit could cause intermittent connections to open, or cause intermittent low signal conditions.
Also capacitors only have a certain life span. 15 years is typical though I've seen some last 25-30. Unfortunately Commodore didn't use the longest lasting brands.
The power supply will be most sensitive to capacitor aging. It takes the most heat and current. Fluctuating power levels will cause a system to hang do to poor signal levels.
And last the chips themselves can age and die. Their lifespan can depend on the way they were made, amount of heat they radiate, the job they do and the reliability of their power supply. There are systems built in the 70's still going today (think arcades), while many others don't live so long.
If you want to keep that Ami going strong another 20 years. have a pro replace all the capacitors (in the power supply especially) and touch up the solder every where. For the chips you can only say a little prayer, keep them cool and feed with clean power . Replacements for many are getting tougher to find every year.
PS.... keep your old systems dry! 10-15 years can corrode connections even in a nice environment with average humidity.
I have a few old favorites that don't see the light of day for years. They are double plastic bagged and tied when stored. A couple years ago I pulled out the old SX-64 to play with friends. It worked and looked as good as the day I put it away 12-13 years earlier. Of course it got all the maintenance mentioned above looooong ago before the storage.
Plaz (reparing old stuff since 1984)