Have you opened what parts of the case that can be opened and carefully cleaned out dust or grit off all of the parts you can reach so there is no interference with any buttons?

Is this happening with a used cassette that you perhaps taped over the little notch to record again and the tape is slipping? Have you looked at the action of the machine itself, comparing it with another machine, to see if any parts appear to be sticking when you push the record button? (Have you cleaned the heads lately? A good thing to do whether or not it has to do with the record button).

What kind and length tape are you using? If it is more than a 90 minute tape (45 minutes per side) it may be the tape is too long and too thin and isn't moving through properly, causing hesitation. This will cause the machine to react the to resistance by turning it self off (just as when you reach the end of the tape).

Do you push just record, or play and record? Has it been so long since you've used this that maybe you need a refresher? Get out the instruction book and read the troubleshooting bit in the back again.

SRS