RCA television shuts itself off

It's "broken". You found out why it was at a garage sale. TVs are not something you can fix yourself. Sounds like a component is OK when cold but is breaking down when it warms up, so the protection circuitry trips. This is so you don't have a fire. TVs are complex electronic devices with hundreds of components in them. Also dangerous voltages that could kill you. Troubleshooting them is a skilled job that needs 1000's of $$$ worth of test gear. Parts are expensive or hard to find for older sets. If a 1993 set is on its original picture tube it won't last a lot longer. Anyway, fixing it would cost more than it is worth.

I would look at it as a sign to go to the library and get a good book to read when you aren't watching tv.

Try taking it apart and (carefully) blowing all the dust off of the stuff inside. Try not to touch anything as there may be capacitors holding charges that could give you a real jolt (while probably not deadly, you might wish you were).

did you ever figure this out? i am having the same problem.

If it works for a while and then stops, it is probably a heat issue in that an electronic component is failing when it overheats.

cjhsa's suggestion of blowing the dust off is the best one you could do yourself since dust could be preventing a component from cooling like it normally would.

If that doesn't do it, then you can either take a course in TV repair, have someone else repair it, or sell it at your garage sale.