If you got another piece of ABS plastic (printer filament, or there are a bunch of normal plastic things that are ABS) then you could mix a little with some Acetone to make a bit of a 'mush', then you could put that all over the area, file it down and drill the hole again and it should be almost as strong as new.
You could also just add a drop of 2 part epoxy (eg. Araldite) over it, and that supposedly has quite a good bond. It's a lot easier, but I'm not sure it'll be as good as using ABS plastic.
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Argh, sorry to hear that.
I guess you never found the bit that came off?
I'm not sure how hands-on you are, but the case is made of ABS plastic, which is pretty common and could be repaired in a few ways:
Hope that's some help!