Difficult to be real definitive without a model number, but in general what happens in automatic mode is the moisture sensor tells the timer not to advance until the clothes are nearly dry, and then the timer starts and finishes the cycle.

I imagine your moisture sensor system is not working properly, and is never telling the timer that the clothes are almost dry and to start moving towards shutoff.

You can try to fix it, and if you want some help post the model number, but my advice in a machine this old is just to use the timed dry. With a little experience you will find you can set it just about right, in fact it may be more efficient this way and save on some energy bills because in my experience folks set the automatic in such a way as to overdry the clothes.