Possible solution (I can't see the comments in the original post; are those facebook comments?). The balloon is attached to a ring, and a thread (A) passes through that ring. This thread has a ring at each end, and these rings are smaller than the ring attached to the balloon.

Finally, a thread passes through each ring of thread A; let's call them threads B1 and B2. Each kid holds one end of threads B1 and B2.

If for example one of the ends of thread B1 is lost by its kid, B1 will slip out of the ring on thread A, and thread A will subsequently slip out of the ring on the balloon. The ballon flies away :)