Well yes, when the light hits a mirror, a certain percentage (say 95% of the energy) bounces back, which can hit another mirror and so forth. There's no limit, but after a few dozen bounces, the remaining light is virtually undetectable.

Really, the exact same thing happens in a standard white painted room, the two differences being that the mirrors reflect more of the light (so that a dimmer light source will suffice to reach the same level of illumination), and that the reflection is directed instead of diffuse (this only changes the shape of the reflected light, not its amount). Maybe you can explain what's confusing you.

Mirrors are not perfect reflectors; some light will be absorbed.

Some of that energy turns into heat every time the photons hit something, but heat is a mix of kinetic energy and light so you do get a fraction of that light bouncing around indefinitely, it's just not in the visible spectrum.

Think of it like dropping a ball an a hard vs soft surface. In both cases things bounce. Even on a hard floor the ball stops bouncing after a while, and in both cases the ball / floor / air get's get's warmer from the balls energy.

The reflection is not perfect; the mirrors absorb some light (and warm up...).

I assume light collides with atmosphere as well. Only in a perfect vacuum, light would travel forever?

The problem with thought experiments is that sometimes you can create a non-physical situation by accidentally introducing magic which invalidates the whole thing.

For example, in this you have a perfect mirror, which is actually not physically possible and would mean violating several laws of physics such as thermodynamics and electromagnetism.

Another common problem is hypothesizing perfectly rigid materials or perfectly flat surfaces, which can't exist in any matter made out of atoms but which could easily beused to violate the laws of relativity.