I much prefer to take your money at poker, mon ami, but thanks for the invitation...
It certainly can be difficult with everything else going on in life. On the one hand, I'm very glad for you that things are going so well (at least, with all that going on, one hopes it's proving lucrative for you), but without question it can cause difficulties when you're going to be out of touch on a semi-regular basis. If it's any consolation, you're not the only one who is being pulled in several different directions these days...
It's not a threat, it's a request, (albeit a sternly worded one) - and it applies to all GMs, not just you. You are in the best position to determine whether you are able to meet the participation requirements of the league - of which responding to communication from the league and other GMs is one of the most important. There are a few things you can do to help minimize the issue:
1) when you're heading into a busy stretch, you can post to the board so people know not to expect to hear back from you for a period of time;
2) If you know in advance that it's going to be a problem on more than just an occassional basis, you can deputize an AGM to help keep things going when you're otherwise occupied, or
3) you can gracefully bow out.
Sorry to have picked on you in this case, but the admin team ends up taking the flack when GMs go AWOL for periods of time. You happened to be the one in this case, but there are certainly others. I encourage you (and them) to think about the above and see whether any of these solutions would work for you.