Yeah, similar rat's nest to mine
That silver bugger on the back side is the quartz and I'm sure there is some black blob-encapsulated IC on the circuit side plus a few passives and that's all she wrote.
Now, what exactly is the problem? Is it consistently running slow or suddenly deciding to jump back half an hour?
Was it always like that or did it go bad exactly next day after warranty expired, as usual?
If it was a sudden failure I suppose you could try to replace electrolytic capacitors or perhaps the quartz (32768Hz most likely) and see what happens. These are probably the only elements that can be replaced in there, anyway. If there are any voltage regulators, check them. Also check the USB power you use.
Build a new board for it? Dunno, I surely wouldn't, but I suppose there may be people who are into such stuff.