The resignation rule is in place for this reason. If you've fallen so far behind in military that you are unable to recover, and you have no chance to get back into the game, the best thing is to just resign. Staying in the game "still having to make turns" is detrimental to the game, as it rewards those that draw the most War on Cultures in Age 3.
Some may argue this is poor game design, and it definitely has issues playing the game live, but for an async online app just resign and move on to another game!
As I've said elsewhere in the forum, TTA is all about creating the best culture engine while maintaining military parity. Always keep yourself within a couple defense cards of the leader, and do you best not to be last in military by the end of your turn.