I have two main hot legs coming into my circuit breaker. One has a steady voltage of ~124V load or no load. The other has some mysterious problem. Sometimes it works fine delivering proper voltage under load. Other times it will drop to at or nearly at 0V under load. When all circuits on the low voltage leg are switched off the voltage will swing from 0V to a large reading. It will keep swinging for about 10 seconds until it finally stabilizes at 124V. I've taken each circuit, except for the 240V circut for the AC as it's winter and never turns on, and moved them to the good line and they all work fine. The utility company came twice and each time they left a note saying everything on their end is working.
What could be causing this?