I seem to have finally traced down the troubles with the forum sending emails. The short version is that our DNS provider made a mistake, which in turn made Google think we were spamming, which in turn made our DNS provider think our account was under attack and lock updates.
Combined with a few changes on Google's side that made this very difficult to repair smoothly, and it was quite a fiasco.
As of now, the forum appears to be correctly sending mails again, and I sincerely hope it "sticks" now. My sincere apologies for the troubles.