The JIT compiler is invoked when a determination is made that a method or a class is being called more than x number of times. The JIT compiler then pre-compiles the method, thus allowing better performance. If the JIT is turned off, then there is no pre-compilation.
Sometimes the JIT complier incorrectly compiles the code, thus leading to problems that you are experiencing. Are you getting any dr watason dumps or user dumps? Generally these files will help identify where the problem might be.
Another thing would be to first identify the method where the JIT compiler is failing. Once this is done, you can skip the compilation of just this method, rather than turning off the JIT compiler, thus not having to compromise on the performance of your application.
I have in the past worked extensively with IBM on two different occasions with regards to JIT compiler problems and have a learnt a lot from that. Feel free to shoot me any more questions you might have with regards to this issue.
Your best bet would be to open a PMR with IBM.