I fully agree with Chris. To check whether that's the reason, check if the CIMs heat-up more than they usually do. If they don't heat up, it won't say much for or against the theory (because from what I understand the situation only lasts a few seconds), but If they do, overload is almost definitely your problem. I want to say definitely, but I've seen enough strange things to not commit to it
Also, if the CG is a bit closer to the left (and the overload theory is correct), it might explain why the left gives out more often than the right.
A related long-shot: do you have a turret?