Why is it, that when a balloon has deflated, it’s not possible to reinflate it? I have some vague idea that it’s to do with the structure of the atoms becoming either less or more flexible, but I’m not sure. My four-year-old daughter anxiously awaits your answers. 
Why can’t you? - I mean whats stopping you from leting the air out and putting more back in - what happens does spacetime come to an end. If so you better tell me because as soon a I find a balloon I’m trying it.
Perhaps you mean a hot air balloon where people fly in it - maybe there are regulations against reuse?
Sure you can. What are you talking about? 
I’ve always found them to be a lot easier to inflate after the first time.
Well, if you let a balloon sit around for a while it seems like all the air leaks out and the balloon gets all wrinkly–but I don’t think this means you can’t untie the end and re-inflate it. 'Course, at that stage, it’s lots more fun to try to pop the balloon, since they get really stretchy at that point and are hard to pop. 
Am trying to think of a situation in which you couldn’t re-inflate a balloon, and am coming up empty-handed. What do you mean?
??? Am I using different balloons to all of you? I’ve always found that once a balloon’s deflated, if you try to blow it up again, it won’t go. This is especially bad with helium balloons, but also with normal ones. How odd that none of you have experienced this. Must be the way I blow…
I can see that it may seem to “take longer” because the balloon has already been stretched out. Therefore not seeing the immediate change in volume/size that you would with a new balloon, and the fact that it could be easier/quicker to inflate.
But if done properly a balloon can be blown up again. (IE: Untied after deflation and unpuncutred.)
It’s possible that in the process of tying or untying the baloon you might have made a small puncture. Or maybe it just acquires a puncture some other way.
so in other words just using your mouth exhale pressure you can’t add any air to it past a certain (small) point?
Maybe you can’t summon up enough lung pressure. Can you blow up a balloon the first time?
It’s my daughter’s birthday tomorrow, so there will be plenty of balloons around. I’ll test out the reblowing and report back. Hopefully then I won’t be feel like quite such an idiot as I do now.
You can blow up balloons quite easily multiple times. I don’t think anyone understands what you are talking about.
Just guessing–perhaps the OP is referring to balloons that aren’t blown up by mouth, but rather “professional” balloons that get blown up at the store via some sort of compressed-air machine? I imagine that such balloons would be difficult to reinflate by mouth.
[Butt-Head] Huh-huh huh-huh-huh-huh… snort… huh-huh huh[/Butt-Head]
Perhaps you’re describing the rubber sticking to it’s self, sorta like there is glue inside it and the flattened halves won’t “unstick” from each other to allow air in. I think such things can happen when the moisture from your breath condenses on the inside of the balloon, and when it collapses after being deflated, the surface tension holds it together or creates a bit of a vaccuum, so that you can’t blow air into it the second time - that or you had something sticky on your lips/tongue and that sealed off the opening. Try rolling the neck around a bit in your fingers to “break the seal” so to speak… this is as close as I come come to envisioning what you describe.