Logan, I thought about entering into this topic with some personal observations, but decided not to as it was running along quite well.
I've had instances of something similar when using a serial modbus line with quite a few slaves. I'd lower the speed b/n calls until it became unstable, then back it off (hmmm "raise it up"?) until it all ran ok. Would do other jobs around the site for the day and it would still be going fine on leaving. A few days later it would fall over, and the cure was a slight increase in delay times. I can only theorise that my initial time was running very close to not allowing the buffer to clear properly, and eventually the accumulated(ing) stuff reached a tipping point where it cracked the poops. All the info being derived was always the same amount of transmission.
Whether this can happen using TCP I don't know, but it does sound awfully familiar. For me, buffers in Unitronics land sometimes pose issues that have to be allowed for.