FPS drops below 1 only in multiplayer on host machine

I have 2 PCs networked together and we typically play multiplayer games against 3 or 4 AI opponents. Anytime after about an hour into the game, the host machine will randomly slow right down to less than 1 fps while the other PC ( despite being a lesser machine) is still running at around 40fps. Sometimes the host machine will be slow for a couple of minutes, then speed up crazily and catch up with the action and get back to a decent fps. Other times the drop below 1 fps doesn’t end and pausing with F3 and waiting for the game to catch up is the only temporary (but unsatisfactory) solution.
Even stranger, if I save the game when it is in this state, when reloading the save - even after a machine reboot - it is still running at this ridiculously slow speed.
I’ve tried disabling and, indeed, removing completely any anti-virus software and have minimized what programs are loaded on startup, but nothing seems to help.
The game has no issues at all on either machine when playing single player.
Has anyone got any idea what I could try to fix this?