This seems to have fixed our issue !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
AIXTHREAD_MNRATIO=1:1 in /etc/environment file
This setting seemed to fix our issue. We are still monitoring but it has been up longer without issues than any time in the past month. We have done more research on this and it is a setting that is part of AIX that goes in the /etc/environment files. It has to do with the relationship between user threads and kernel threads. The default for AIX has something like 8:1 user:kernel threads. This setting makes that 1:1.