You might have better luck getting a reply on the E-flite forum, as there will be more MCX flyers there.

But it sounds to me like it's either a motor (most likely - does one of them get hotter than the other?) or a 4-in-one (or do those have 3 in one's ?) problem - something with the gyro or one of the motor controls in it.

If it's doing the exact same thing with 4 different batteries, it seems highly unlikely that all 4 would fail in the same way at exactly the same time.

If you flly it until you lose control and then change the battery and immediately fly it again what happens? How about if you fly it until you lose control and then unplug and replug in the same battery? Does it fail immediately, or after 1-2 minutes the second flight?

If it immediately fails after the first 1-2 minute failure and reset, then I'd suspect a motor problem that's causing it to heat up... then when it cools down it flys ok until it heats up again. Could be the same issue with a speed controller in the 4/3?-in-one.