rapid degradation after postmaster restart

I'm trying to troubleshoot a performance issue on an application ported
from Oracle to postgres. Now, I know the best way to get help is to post
the schema, explain analyze output, etc, etc -- unfortunately I can't do
that at the moment. However, maybe someone can point me in the right
direction to figure this out on my own. That said, here are a few details...

PostgreSQL 7.4.1
bash-2.03$ uname -a
SunOS col65 5.8 Generic_108528-27 sun4u sparc SUNW,Sun-Fire-280R

The problem is this: the application runs an insert, that fires off a
trigger, that cascades into a fairly complex series of functions, that
do a bunch of calculations, inserts, updates, and deletes. Immediately
after a postmaster restart, the first insert or two take about 1.5
minutes (undoubtedly this could be improved, but it isn't the main
issue). However by the second or third insert, the time increases to 7 -
9 minutes. Restarting the postmaster causes the cycle to repeat, i.e.
the first one or two inserts are back to the 1.5 minute range.

Any ideas spring to mind? I don't have much experience with Postgres on
Solaris -- could it be related to that somehow?

Thanks for any insights.

Joe