Obviously it's a psychological thing, but let me give reasons why I would push it again.

I think it's less about making the thing work faster and more about satisfying ourselves that we're doing enough to make it work. Let me use a hypothetical situation, if you're being chased and you manage to get to an elevator and you get in and press a button but like all elevators, it's sluggish to react and then you see the person that's chasing you running towards the elevator, Your instinct of self preservation won't let you just stand there and do nothing but in the real sense there's nothing you can do, so the brain makes us do the only thing we can at that time, and that's to push the button again, at least we satisfy ourselves that we are doing something about the situation.

It's the same thing with when you're just standing in an elevator and it's delaying, your brain will tell you that something is wrong and pushing the button will fix the issue, simply because the thought of standing there and doing nothing isn't acceptable.

It could also just be a function of impatience, alot of people deal with their impatience by pushing the button again. This sorta restarts the timer that they have in their mind for when the elevator should close and start moving. If it moves immediately after they press it again, then the brain will record the second time they press the button as the reason why it moved.

To be honest there are alot of reasons why people would push it again, I'm just giving you reasons why I would do it, it may be different for others.