1993 Honda Civic car won't go

Hello, my problem goes like this: While driving from work stopped at a red light, when light went green car would not go. As you push on gas pedal, rpm goes up but gear seams not to engauge. So I put it in park, turned off car, started car back up, put it in drive and drove off just fine. Few miles down the road car started to lose speed, rpm went up as I stepped on the gas but vehicle just keep slowing down. Pulled over shut car off and back on, same thing happened. This happened all the way home that day, about 6 times in a 32 mile trip.
I never had any trouble with the transmission untill this happened. Not even any slippage. Fluid is clean and does not stink, and there was no noise (grinding or otherwise) when this happened, and I still don't hear any when it is driving. I've look all through my haynes and can't find anything that would cause this unless the whole tranny has give up on me. I kinda live out in the boonies so a mechanic is not close. I'll be on my own for this so your help will be very welcomed. Thanks, Ron in Florida