I can only contemplate these two errors to be related. When ORA-3113 occours, it would drop the connection. Which inturn could cause the other.
Make sure that your pocedure puts less load on the CPU. You might want to review the procedure and see what areas that contention is comming in from. Check also your network to make sure that the network was able to handle the load, without dropping out.
Also make sure that your DBA/System administrator does not kill any long running/CPU intensive processes. Or check to see if there are any moniitoring scripts that would get kicked in during these periods or gets run regularly, that monitors the CPU resouce usage and would kill/abort the processes that run beyond certain limit, for certain period of time on certain days.
These are some of the things that I can think of now.
Life is a journey, not a destination!