I had the exact same problem and even took it to an Apple store, which said the cost of fixing it, given it was an older first generation unibody, made no sense. So, I was on my own.
Following suggestion I found online, i did the following:
1) Carefully took pix of everywhere there was glue inside the case.
2) Scraped out the old glue and noted its locations.
3) Sanded these locations lightly with high grit paper (600 I think). Vacuumed carefullly.
4) Treated these spots with a weak acid to etch them, I think I used vinegar.
5) Wiped it with rubbing alcohol to clean all residue and aluminum dust.
6) Using the photographs, I carefully applied JB-Weld Liquid Steel Epoxy to the same plces the glue was located, not just gooping it in, but not just putting a few touches of it either. Use the JB-Weld that takes the longest time to cure. (That is the strongest.)
7) Clamped it carefully, just enough to hold together, and make sure you don't let the case skew while clamping. Undue and realign it if needed. Left it two days.
Result: it worked. The case cover is back on, the screen is not coming loose, and it has held up 6 months now. Even getting very hot at times. It works.
NOTE: I do carefully baby the hinge, i don't just open and close it like when new, i continue to press down on the back and slowly open to minimize pressure on the hinge and reverse this when I close. Anyone who has the loose hinge knows what I am talking about. IT can't hurt to keep it stressed as little as possible. That said, I have forgotten one or twice and just slammed it shut or yanked it open. No problems.
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