Too many open files

I am running PosgreSQL 7.1 on Redhat 6.2 Kernel 2.4.6.

Under a pretty heavy load:
    1000 Transactions per second
    32 Open connections

Everything restarts because of too many open files.
I have increase my max number of open files to 16384 but this
just delays the inevitable.

I have tested the same scenario under Solaris 8 and it works
fine.

Is there anything I can do about this?

Darin