The game freezes if there's nothing coming through from the remote player(s), meaning that it is unable to proceed without dropping connection to player(s). Timeout regulates how long the game waits this way before giving up.
Amount of things going on has very little significance due to technical aspects - since the number of objects gets very high late-game, networking is done closer to how RTS games usually work - transmitting actions instead of positions.
My suggestion was to try setting the timeout to a very high value (e.g. 3600 = a hour), and seeing if it eventually comes back or not. The technical side is as simple as it gets (asks Steam to send data back and forth; pings twice a second if nothing comes back), so it is unlikely that anything can be done on the side of the mod; Restarting Steam sometimes fixes particularly strange issues with it.