91 integra transmission issues?

i just recently bought a mint condition 91 integra gs with 131k on it ..automatic... anyhow the car will drive for about 10 minutes and then will loose all gears... no drive or reverse... when i shut it of and restart it it works fine again for about the same amount of time... i dont believe it to be internal or mechanical as i do have some experience with trannies,,,, so im thinking shift silinoid or something but im really not familure with these cars.. any help would be very greatly appreciated
thanx