Well you could get a Paid Account...
Depending on your motivation you could consider switching to a different server. Everyone would like to have a higher turn storage I am sure but the way this game is set up the faster servers have a lower turn storage max and the faster ones are smaller. On a slower server you can go do other things for a couple days and then come back and you won`t have lost any turns, so you can still be competitive even if you can only play once every coupla days. On the faster servers, particularily RT, you are constantly "wasting" turns if you don`t stay logged on so in theory you should be on nearly every waking minute or else you will fall behind :P
TEXT WALL :O