I don't know if this would affect your specific problem, but I seem to remember that with my 60D, somewhere in the menus, there were some settings that allowed you to register your batteries with the camera body. Though it's been a few years since I've bought any new batteries for this camera.
I've registered both Canon and Wasabi batteries with the 60D and the battery meter seems to read properly with all of them. I seldom shoot so much that I need to change batteries in the course of a day's shooting so this might not be the best way to test for a problem like yours. But the Wasabi batteries seem to have the required "chip" to register with my camera. It treats them the same as it does a Canon battery.
Registering the batteries seems to let the camera remember the state of charge for multiple batteries when last used. Maybe inserting an unregistered or "unchipped" non-Canon battery causes some confusion in this feature. Your best bet is to stick with Canon batteries if possible. If you must use an off-brand battery, don't be tempted by low price alone. I've had good luck with 3rd party batteries but I wouldn't consider using one that was 1/4 the price or less than the Canon product.
