32nd Oracle Process Hangs

I am running into a strange problem where attempts to log into Oracle hang.

Monitoring the number of oracle processes shows that we consistently get this problem on the 32nd process. Once 31 Oracle processes have been created, all subsequent login attempts hang (until one of the existing 31 exit). Even if I use SQLDBA and connect internal, when I try to bring up one of the monitor displays, it hangs.

I have talked to Oracle and so far they cannot explain the problem. They seem to think it is an OS or network problem. I don't think it is a network problem because

1. No one has any problems with the network except with Oracle
2. I tried accessing Oracle from the server for the 32nd process and it hung (because I was on the server I don't believe any network resources were used)

And I don't really think it is the server OS configuration (Ultrix 4.3a) but I suppose it could be. Does anyone have any suggestions or clues? We are using Oracle 7.0.12.2.0 on Ultrix 4.3a.

         thanks for any help!
              jim