Problems like this are quite commonly due to worn drive belts, as this alters the tension of the tape and the player can 'think' it has reached the end of the cassette, thus causing it to stop.
This should be easily repairable by a local tv,video repair man,although get a quote done first as with the price of video recorders ever decreasing it can sometimes be more economical to buy a new one.
Its a wonderful disposable world of consumer goods!
Wayne
April 2004