:( Increasing the number of states did not seem to do anything. Looking at the states table, it might have been possible that the number of states was exceeding 10,000 at certain times of day. But now that I've set it to 20,000, I don't think that is the problem.
I've also tried tweaking the apache server KeepAlive setting and also turned KeepAlive off. No luck there either.
I guess if no solution presents itself, I'll have to switch load balancing to LVS or something.
The two pfSense boxes are Dell 1850 dual Xeon 3.4Ghz with 4GB of memory and a 2-port Intel PRO 1000 network card for WAN and LAN.