[LeTharg]

There is a proposed enhancement on the to-do list for PBW to allow you change your state so the game won't wait for you when you will be unable to play.

Two suggestions:
1. Get someone to play your turn for you with permission of your game admin. It will be much much better than letting the AI play and it won't hold up the game.

2. Or else if you are only going to miss 2 or 3 turns, then go into the empire options and ministers and set the flag that tells the AI to do nothing in simultaneous games. It will still do terrible stuff but much less than otherwise. If you fill all your queues (construction, research, movement etc.) it won't change your orders. It will mess up your designs and take every opportunity to destroy your position. But it is better than giving it a free hand.