Should time matter in models of our universe?

If we accept that there'll ultimately be no free energy left in the universe, we'll reach a state where infinite time will be able to pass by without any change in the universe, therefore any event that has a nonzero chance to happen will happen.

The one single exception to this is an event that changes this state, if such an event occurs we no longer can say that everything will occur given enough time (we no longer have infinite time)

I'm very obviously a layman, but I can't see why this wouldn't happen unless the probability of an event that has the potential of creating free energy is zero.