dual redundant connection disconnects

[k000k]

I am having a problem with MSN at work. I have 2 connections to the internet with different IP's for load balancing/failover. TCP connections are created over either connection more/less arbitrarily, it depends on traffic, etc.. This setup is causing the following problem:

A TCP session is being created over one connection, and when certain traffic is sent (PNG for example), it's sent over a NEW TCP session, which is sometimes over the other connection/IP. The MSN server sees this as me "logging in at a new location", so the next packet I get is an RST, followed by my SYN, msn's SYN/ACK, my ACK to establish the new TCP session. Then it exchanges version info, re-downloads my contact list, etc. because I am logging in again... MSN connection is killed and re-established over the other connection, until it happens again.

The connection keeps flip-flop'ing from connection to connection, with a lengthy (6 second) disconnect-reconnect every time. During this 6-second outage, my contacts have no idea I dropped out. Their chats to me while I'm down are being dropped with no indication of error on their end. I have verified this via packet captures on the PC's and the external internet connections. OS and client are irrelevant.

MSN is not required for workers here, therefore I will not be allowed to modify rules that determine how traffic gets routed. Ie, I wont be able to force all MSN traffic out one particular connection. Any cure to this problem?