Yes, but you have to fix it really carefully, and I wouldn’t want to try it myself.
In a way, a balloon is not too different from a bicycle tyre – they are just rubber or plastic filled with a gas, in this case air. You can fix a flat tyre by putting a patch over the hole and sealing the rubber/plastic and I have bike tyres that were patched over 10 years ago and still can be inflated. The fat that balloons are made from thinner plastic and, when popped tend to burst into little bits makes the challenge of patching them up a lot more difficult!
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