Kenmore 110 Washing Machine doesn't spin automatically

My heavily used Kenmore 110 Series Washing Machine stops and turns off before the rinse and spin cycle. Has required that I run a separate "rinse/spin" which it then completes. This has occurred 3 times this week. Lint trap at end of drainage pipe in since is clear. Doubt pump is problem due to ability to ultimately get it to spin. Any suggestions?