You're using self-stick tape on dry sheetrock, right? You don't put mud under it like paper tape. I know it's obvious, but just trying to eliminate possible issues. If you're doing it dry, sounds like you have tape that has lost its tack due to being exposed to dust from cutting or sanding or you have dust on the drywall joints. Also, if you wait too long before mudding it'll lift.
For the tape showing thru, you might not have enough joint compound over the tape and also not have it feathered out far enough. I am not a DW expert but just repaired extensive gouges and gaping holes, filled in a medicine chest space and filled in an old fluorescent soffit for can lights. I had the compound feathered out 6 to 8 or even 10 inches per edge of the joint and it the job came out very well. Hope this helps.