If in fact you have any. Use it, that's what its for. Any attempt to fix or correct may void the warranty. Of course if the warranty isn't active, then you can fully inspect the GPU, in hand. If you find a loose HDMI port, etc., then a simple touching of the solder iron or flux/solder use may correct it However, I'm not there and haven't a clue to physical assessment. I hope we're talking about a desktop GPU and not some laptop. If laptop, I suggest you visit the local tech shop. if the problem isn't resolved, then a replacement card is in order, probably the cheapest repair if no tech involved.
The HDMI port on my friends GPU is loose and we have to prop the card up with dvd cases and wiggle the cable around to get it to work. The card is sitting in the right spot meaning like where we tightened the screws on the case, we tried multiple spots and the current one works best. I'm almost certain that the problem is the port inside the card. Is it safe to open the card up and try to readjust the port?