If you want avoid this in the first place it would be a good idea to not take arms out and put them back in.  I think that's what makes it happen.

As far as fixing it, that does sound like a long shot, by i don't think that it would be entirely impossible.

The first idea that comes to mind is heating the LEGO up a whole lot and fusing that plastic back together.  Of course, heating it up to such a high temperature would likely damage other parts of the figure.

Yeah, I try to avoid swapping out arms.  I don't ever recall doing that for the blue suit, though, and there are a few that seem to have cracked naturally despite me never popping the arms out (that I can remember).

To be honest, I'm not sure if heating would work.  It's a tiny area to heat, plus the plastic would easily deform when heated.  I'm personally thinking of somehow gluing the crack, but I'd have no idea how to get the glue into the crack, and not getting it anywhere else or messing up the arm socket or other areas.

If you do end up using glue, you could always file it down if you got it on the outside of the minifig too. And there is  model paint if you need to fix some color damage.

The only solution I could find is to try gluing it from the inside.
No visible mess, able to get more glue in and on it, but even then it's not always successful.

I wish you the best of luck on fixing it.