For rare events is made a reset to the initial bet. Doubling does not go on forever, the loss after the last unsuccessful bet is overlaps by subsequent successful ones which will go after the reset. There is a certain balance in the system of doubling bets, at some moment it ceases to work in plus and begins to increase the loss in progression.
What people also sometimes forget that each bet is actually individually separated. So, even tho it looks like there is a small chance of x1 happening twice in a row it is also as possible as anything else. There is literally a 50% chance of being x1 on each bet and not being x1 each bet. There is a gamblers fallacy that looking at odds you go and say if it happened once it is rare that it happens again but those two bets have equal chances of being x1.
I can understand why people think it is rare and I do see it rare too but it is actually not, both those bets have the same amount of chance of being x1 and have nothing to do with being back to back. Same goes for good ones too, there is a chance of x10 happening twice in a row too, so don't look at it only from the bad side.