My transmission is working fine when cold.  After first starting, all gears
shift normally for about 5 minutes.  Then it starts to slip. After 10
minutes, it won't catch in any gears - forward or reverse.  Then if I let it
sit for awhile, it will start catching again.

One mechanic said he heard a whine and said it was a pump failing.

Before we crack it open ($300+ minimum), I wonder if anyone else has had
this happened.  One thought I had is that residue circulating while running
builds up and blocks some passage, causing the pressure failure.  I'm not a
transmission guy - but wonder if trans can be pressure flushed without
removing from the car, on the chance that flushing might cure the problem?

Thanks in advance!!

Bob