Infrastructure Software

I having been running a java process in the background and was finding that occasionally the process was dying when the exited the session. I found that when I exited the telnet session (the Solaris machine is at a remote location) cleanly (using exit or logout), the process would remain running. When exiting uncleanly by closing the telnet application directly without a logout or exit command, the process would die. I then found the nohup command and tried using it, but got the same behavior. All of my research indicates that without the nohup command, all background processes should die when the user exits (clean or unclean), and when using the nohup command, all background processes should remain running when the user exits (clean or unclean). I am confused why I am seeing the same behavior regardless of using nohup. I have tried different shells and found similar behavior.

In addition, what is the best way to persistently run a background process with high priority?

Thanks,
Kevin