My experiences showed something entirely different - the reinforcements are delayed when the weather is bad, for example heavy snowfall or heavy rain with fog and limited visibility. i never noticed that this is random, only really bad weather condiotions delay reinforcements.

i play rtw.exe or alex.exe, units scale huge, highest detail, and i sometimes fight multiple fullstacks in one battle - so i'm sure it's not fault of a weak system. Pretty sure it's the weather. That would seem realistic, too.