shyvana stops auto attacking randomly during Q/W/E cast

Are you referring to her stopping in the middle of the animation during the instant they're cast but other wise be fine? Some abilities do that, her Q specifically, being an auto attack augment, is what's called an 'auto attack reset'. Used right you can actually do quick double-hits for some extra bit of dps. (Apologies of you already knew this, can't tell how much someone knows, you know? :P)

Otherwise most any ability that has an animation, like Shyvana's E, will interrupt an auto attack. It's something to keep in mind for clutch fights where an auto attack can mean the difference between a kill or a get-a-way