I play on Insane, so in the early and mid game, if an opponent has less than double my power rating, it means another opponent is killing him.
I only restart when my defeat is imminent. For instance, if an opponent is taking down my cities, or if they've got too many armies in my territory to keep casting Tremor to stop them. In the game I won on Ridiculous, I was on the bottom for so long, but I'd built such a strong economical foundation, that in the late game I was able to vault forward, overtaking everyone. The point is, if you're playing on a higher difficulty setting, being at the bottom of the power chart for a long time is normal.
Another thing I've noticed is that, I play on a large map but with 8 opponents, and often my opponents will not expand beyond their first city, even the one on top. So, even if you only get one city, you can still make it. Just don't lose it.