I had exactly the same problem with an iPhone 4. The replaced phone then started to give me a problem whilst taking calls, people couldn't hear me. In the end I stupidly just bought an iPhone 5, the screen then started to give me problems again out of warranty (typical). Last apple iphone I ever bought.
I have little faith in refurbished units. I have an MS Elite Controller V2. It had unresponsive buttons and stick drift. MS accepted it back no problem and sent me another unit (refurbished as far as I can tell)
this also has two issues. It switches itself off now and then and has one less responsive paddle. But no stick drift
. I think these have a history of issues though and I think the consoles less so.
I understand your concern regarding shipping it back. If anything might be better to just get your money back if you qualify for it (just my opinion). Buying direct from MS will allow you to get an extended warranty. Not that I got an extended warranty or did I buy my SX direct from them but I wish I had. Mine was from amazon, just down to availability at the time. But they have always been pretty good regarding returns (as long as it is within warranty). But this then leaves you with the task of finding another unit.
Bottom line if your current unit is showing signs of not being 100% best to get it sorted now as potentially the issue could get worse especially if it actually is a hardware related issue. It will also be at the back of your mind.