You have to win 3 rounds with 1 ammo of each weapon, and since there's anti-stockpiling, you will never see again an ammo you've used.
If a disconnection happens, rounds played so far aren't blanked. Start a new game with one (or more) blank rounds where you have to use the previously used weapons, so you can then continue the game with just the weapons you didn't use. Taking notes of the used weapons or having the replay of the game before the interrupted one in a separate W:A process would come in handy in this situation. Of course, it would only be fair to take turn order (i.e., who is supposed to play first) into consideration.