I suspect that dead spots are developing in the timer...
It's hard to suggest this because the information available is not precise, but dead spots are very common in the timer that was used in many of these machines, and they typically are seen in high current draw portions of the cycle such as spin.
Let me describe as best I can what typically happens as dead spots develop and worsen:
First, a brief interruption in motor operation will happen as the timer advances. It is usually so brief at first that users don't notice. Since I typically hover near my machines when they are running, and I enjoy listening to them, the sound of a quick motor on-off-on again is very noticeable to me. This behavior gets worse as the timer warms up, thus they happen more in the final spin vs. the first one. If several consecutive loads are run, the first load on a cold timer may not exhibit any dead spots, whereas the third load may have several. Let the timer get cold and they will be gone for a while again.
As the timer contact continues to wear, it will cause the motor to turn all the way off. This is unmistakeable to most. The timer motor and escapement continue to run, so the timer will advance and turn the machine back on and resume where it left off.
Eventually the contact will get so bad that it stops the machine cold. The user can usually giggle the timer knob and make the machine come back on. On really bad timers where users let them go way too long, there will be dead interruptions at every timer increment.
The Mallory produced timers from early - mid 80s machines seem notorious for this in my experience with these machines. The CCA / Singer / Eaton timer did not seem to do this, but had other issues. Ironically, the plentiful production made in the 1980s of the few variations on this machine seemed to all have a Mallory timer. My mother's late 1982 machine, and several of mine from 1980 - 1986 have done this and I tend to expect dead spots when checking a machine unless it already has a new timer or is very low use.
If this describes what is going on, I would replace the timer. The switch bank in the timer can be worked on or replaced, but a timer swap is a simple and quick fix for someone who is not interested in disassembling the timer.
Let us know if this describes the issue!
Gordon