Oracle.exe (SHAD) process keeps increasing
If you're on Windows and have DCD (dead connection detection) enabled then this could be relevant to your case.  There is a note on Oracle support that talks about poor implementation of DCD on windows leaving behind a bunch of shadow processes.  Without going into details as I don't think I can republish that info here, the solution was to disable DCD.  So keep a monitor on the number of shad processes and disable DCD in sqlnet.ora.  Fairly quick and painless to test if that is the cause..