Wow, that's odd for a Whirlpool - the motor usually runs continuously as it shifts from agitate to spin.  Is the timer advancing normally during wash?  Does the machine stall at the neutral drain?   If so, does the timer continue to run? Does this happen at the end of the wash phase only or does it also happen at the end of the rinse phase of the cycle also? 

My gut feeling would be that there is a timer issue - possibly bad contacts...