I was having this same issue and none of the posted solutions was working. In the end, it turned out that it was because the filename of the avatar image was the problem (I presume too long).
Basically, I was testing uploading an autogenerated filename (32203c6ae1bc3723a3432a38b1185490-bpthumb.jpg).
This failed with the non-descript error: There was a problem cropping the avatar.
I shortened the filename, and BAM! all works fine.
In that none of the posts I’ve seen around this problem suggest the filename as being a problem, I thought I’d post my solution.
(May be worth adding an error check to bp-core-avatars.php ?)
