A balloon will only stay inflated if the pressure inside the balloon is greater than the pressure outside the balloon. As the balloon rises, the air pressure outside the balloon decreases, which causes the balloon to expand. This expansion causes the pressure inside the balloon to decrease, which eventually causes the balloon to pop.
However, if the balloon is made of a material that is strong enough to withstand the expansion, then the balloon will not pop. Such a balloon could stay inflated indefinitely, provided that the air pressure outside the balloon does not exceed the pressure inside the balloon.
In practice, however, it is impossible to create a balloon that is strong enough to withstand the expansion of the air inside the balloon. This is because the material of the balloon would have to be infinitely strong, which is impossible.
Therefore, while it is theoretically possible to create a balloon that never goes down and pops, it is practically impossible.