Wow... this is a long standing bug that I should have fixed a long time ago!
I have known forever that you couldn't create more than 238 Exodus output files. Yes... that means that if you are doing adaptivity you will get an error when you try to create the 239th exodus file to write out your solution!
For whatever reason this never bothered me enough to fix it... until yesterday when I finally had a problem I that I needed to run more than 238 timesteps of with adaptivity! So I investigated this morning and found it to be a fairly simple error in ExodusII_IO_Helper::create()... we were calling ex_create() and then _reopening_ the file with ex_open()!
ex_create() _opens_ the file when you create it... there is no need to call ex_open()! What I think was happening is that we were essentially opening each file twice... but losing one of the descriptors such that we could never close it... thus to Exodus it would look like we had a TON of open files. I'm guessing that for whatever reason Exodus can't have more than ~240 files open (I still can't quite figure out why... but I didn't look through much of the ExodusII source).
So the fix was trivially easy... just remove the call to ex_open(). Really should have fixed this a while ago ;-)