After some further research it looks like the crashing may be related to Date Execution Prevention (DEP). The BEX error is produced by the DEP subsystem. I tried adding Acrobat.exe to the DEP exception list but a message is displayed stating "This program must run with data execution protection (DEP) enabled. You cannot turn off DEP for this program."
Is it possible that there is a bug in Acrobat that's causing it to not be fully compatible with DEP?
Note that since the original post, Acrobat has crashed once more with the BEX error.