Multi-touch randomly breaks on WP8 when not plugged in to PC

I'm developing a game where you have to press buttons in the correct order: there's one button on the left side of the screen and one on the right.

If you press one button, it works just fine, but if you press both at the same time, some times the phone will not register one of the button presses. It happens ~15-20% of the time. This occurs only when the phone is not plugged in to my computer. If plugged in, everything works as it should.

I'm using a Nokia Lumia 620 to test this on, I have also tried it on an old iPod where there were no problems at all.

Does anyone have an idea of how to get around this? Any mysterious battery-saving features I need to somehow disable?