Almost anything you can imagine can be accomplished but it is often not practical to do so. Why do you believe storing H2 inside zeolites is any better than putting it in a steel tank or a balloon or perhaps a metal hydride?
Hydrogen is smaller than almost everything else. It is very difficult to store for long periods of time because it will always find a way to escape.
Rick Manner Thank you for your comment. I meant by storing hydrogen using zeolite is storing for a short time after capturing it from reactions forming it.
The zeolites I am familiar with are used to adsorb non H2 components and allow pure H2 to preferentially pass though. This is how the Pressure Swing Adsorption H2 purification process works.
There are many places that store H2 in high pressure tanks and even in large caverns. But there are always some losses because H2 is very small molecule that can pass through almost anything you try to use to contain it.