Assuming neither player is much better than the other...

You 2:1
40% win outright + 0.6 x 0.33 chance of winning if you lose (now you are outstacked 2:1)= 60% chance which is worse than if you fold.

You 5:1
40% win outright + 0.6 x .67 chance (now you are down to 2:1) = 80% chance of winning
which is worse than the 83.3% (5 in 6) you would have if you fold.

So, 40% is not enough. I am pretty sure (without doing math) that 50% is exactly even with zero blinds.

If the blinds are 10% of the total chips (so 3000), then it becomes much closer (because, for example, in the 5:1 case, his chance of future winnings goes up 60% if you just fold!)

It's all about the blinds. Say the blinds were like $1/$2 and the stack sized are like 20K to 10K. If the short stack pushes every hand, just fold until you get a good hand. You'll get one long before he catches up to you. Obviously, if he's not pushing every hand then you actually have to play poker instead of algebra.