I have an older, may 10 year old, Whirlpool washing machine. The machine agitates OK in the beginning but then starts to make a bad noise that gets worse the longer you let it go until finally it stops. If I leave it for about a half hour or so and try again it will start and spin out. We just replaced the motor coupling and just don't know what to try next. Could it be the dogs?

The "dogs" are in the agitator and not the problem. A better description of the noise would be helpful, but it sounds like you may have a bad motor, cutting off on the motor overload which then cools off and allows it to run again.