Why doesn't Martingale work?

In my manual i state that the Martingale System doesn't work. Why is that? In theory if you play a 50% game chance, if you continued to double your bet every time you lost, you would eventually recover your losses and win some money. The problem is, if your initial bet is 1, you would only have about 7 bets to play: 1-2-4-8-16-32-64 $. Every table have a maximum bet limit, and it's usually 100$. In these case if you lost 7 times, you would be out of the picture, and you would lose 128$. You would have to win 128 times, to recover your lost.
And a streak of 7 losses will always come. Don't play the Martingale system. It only works with unlimited money, and unlimited bet limit. and that doesn't exist.