Question

why we can balance cycle when it is running but can't when it is at rest

Answer 1

Running cycle has more momentum than a stationary cycle hence it is easier to balance a running cycle.

Answer 2

we can't balance when it is at rest because it have only two wheels and don't have the support that's why we loose our balance .
while cycling we can balance it because we were balancing it with the help of piedel and therefore don't loose the balance