I have never seen that exact issue, but almost all electric washers I have used end up having a problem with the washers own GFCI breaker on the end of the cable (small box near the plug end that has a reset switch on it). I would use your multi meter and check to see if you are still getting a full 110 from the cable, before the motor, after it turns off on your first use. Those plugs can stop power without tripping the exterior switch on them, then randomly work again. The solution is to cut that off the power cord at the GFCI and wire in a new one or just a plug. If you use just a plug, you will have to make sure it is only plugged into an exterior, working GFCI for safety. They add those for extra safety, as not everyone has a protected outside circuit. Exterior gfcis can also fail and still pass power but not work correctly and trip off. Those small, cheap plug in testers have a button on them that allows you to test any GFCI by tripping it and then you reset manually to confirm function.