As mentioned by @Steven. You'll want to get yourself an ammeter, and figure out how much current the appliance is drawing. While shopping for the meter, you'll want to look for a "Peak Hold" feature (though it might go by other names depending on the manufacturer). This feature will allow the meter to retain the highest measured value. That way you don't have to monitor the meter.
Remember when using the meter, you have to clamp it only around one of the circuit wires. If you clamp it around the cord; for example, you'll always get a reading of 0. The best way to do this, is to clamp the meter around the ungrounded (hot) conductor in the panel where it connects to the breaker.
Circuit breakers include overload protection, which is also known as thermal protection. This is typically a bimetallic strip, that pulls the contacts open if it gets too hot. This type of protection is time delayed, since the device has to physically heat up. If the current through the breaker is really high (but less than what trips the magnetic protection), the device will heat up quicker and react more quickly. In your case, however, it's more likely that the current is just high enough to cause the breaker to slowly overheat. This would explain why letting it cool down (waiting), would allow it to run longer once reset.
Your intuition could also be correct, and a loose connection could be exacerbated by the heating due to high current draw.
In either case, an ammeter will be a useful tool to start diagnosing this issue.
NOTES:
- If the breaker is a GFCI breaker, the sanitize cycle could simply be leaking too much current.
- If the breaker is an AFCI breaker, the sanitize cycle may be doing something strange that the AFCI is picking up.
- Thermal protection in circuit breakers can be affected by the ambient temperature, and the temperature inside the panel. So if the panel is in a really hot location, it could trip before it typically would/should.
Update:
Now that it's clear that the circuit is protected by an arc-fault circuit interrupter (AFCI) circuit breaker, I'd like to change my answer. While an ammeter is useful, and testing the max. current draw might be useful. I suspect that the machine is doing something during the sanitize cycle, that the AFCI doesn't like.
The symptoms you describe are consistent with a failed lower element.
An electric water heater typically has two elements (and two thermostats). Only one element operates at a time.
Under normal operating conditions, the lower element will turn on when water is drawn out of the top of the tank and cold water enters the bottom of the tank. When this water at the bottom of the tank is sufficiently heated, the lower element turns off. The upper element is not activated at all.
If a large quantity of water is drawn, perhaps in excess of 50% of the tank capacity, the upper thermostat will detect cooling in the upper portion of the tank. This will cause the upper element to turn on and the lower element to turn off. When the upper element heats the upper part of the tank sufficiently, it switches back to the lower element to complete the heating cycle.
If the lower element or thermostat fails, the lower portion of the tank will never be heated. This significantly reduces the effective capacity, as only the upper portion of the tank will be heated.
If the upper element fails, you may continue to get hot water as long as the upper thermostat is not triggered. But once the upper portion of the tank cools and the thermostat triggers the upper element to come on, all heating ceases. The lower element will never come back on (because the upper thermostat is calling for heat from the upper element, which fails to provide.)
Another less-common possibility is a broken dip tube on the cold water inlet. Normally, the cold water inlet is at the top of the tank and just inside this inlet, there is a tube that extends to the bottom of the tank to direct incoming cold water to the bottom. If the dip tube has broken, cold water now enters the top of the tank, where it mixes with hot water and cools it off.
Before replacing the element, check the sacrificial anode. This is an aluminum or magnesium rod about 3/4" diameter with a steel wire core. It helps prevent corrosion of the water tank. If the rod is more than 50% consumed replace it along with the element. If it is completely consumed so that only the wire core remains, replace the entire water heater.
(If a sacrificial anode is allowed to be completely consumed, we can assume that the tank has begun to corrode and will need to be replaced soon. Better to replace the tank before it leaks than have to clean up water damage from a flood!)
Best Answer
It would be rare indeed, and obviously it would matter what your specific brand and model was.
In general, assume no. If you want a warm-water wash with a broken hot water heater, heat up some water on the stove and pour it in as the machine is filling.
On the other hand, you might find that you can get perfectly decent results with cold water.