I have on the well from hell (150days over AFE!!). The completion came out twice, we were investigating outer casing strings leaking, tubing hanger leaks, leak testing with inflatables in the tubing, and .... it was horrible!
Anyway, you say it's a new well. Did the tubing pressure test? How did you test the tubing (against a plug set in the end of the tubing or against the casing before you perforated?). Did the A annulus test? How did you test the A annulus? Do the results of these tests tell you anything? The other thing to consider is the completion architecture: do you have any sliding sleeves that oculd have failed? Any PBRs that could leak and so on?
Ultimately, you may have to retest the tubing against a deep set plug- most completions have a nipple at the end of the tubing for this purpose- while monitoring the A Annulus. Then test the A annulus, while holding pressure on the tubing and then after letting the pressure off the tubing. If there's no pressure loss in the tubing during teh tubing test (or pressure gain on both the annulus tests) it's probably a packer. If you see a tubing pressure gain on one of the annulus test, then you've proabably got a problem with the jewellry somwhere- these often have chevron (ie paired one way) seals. otherwise you're in our situation- looking at the outer casing strings and so on (eventually our problem was traced to an out of tolerance wellhead).