Perhaps Jeff’s non-interruptible code is a routine for processing some data received from that interrupt. If so, you must buffer the data and let the processing routine to get data serially. However if the interrupts not burst – data will overwrite (a mailbox will be more appropriate).

Hope this help,
Nic

P.S. Eric here there is a justification for using a RTOS: the processing routine can be a task that receives messages from a high priority task (interrupt routine)