the light would fade, as mirrors are not perfectly reflective and the medium that the light is traveling in will also absorb energy. There are dielectric structures called photonic crystals which can theoretically have a 100% reflectivity, and you'd have to run everything in a vaccum so you don't get absorption in your medium. But, you still have to inject the laser beam somehow, which means you have to have a hole and light will eventually leak out.
Intensity is power/area, so to intensify a laser, you can simply pass it through a single lens, it's not really necessary to use multiple lenses. (although the intensity is only increase at the focal point) Keep in mind that increasing the intensity doesn't mean that you have necesarily increased the power of the beam. Using a lens simply means that the spot size has been decreased.
You're probably thinking of amplification. That is, a way of putting more power/energy into the beam itself. This can be achieved using an optical amplifier. Basically, you make an optical cavity and fill it with a material that you can pump to a high energy level such that the transition energy corresponds to your lasing frequency. But this is aways an active process, it consumes energy. There's no way to maintain the power of the light inside your container unless you add energy into it.
Basically, the object that you're thinking of is a microwave. The sides of a microwave are metallic and are pretty highly reflective at microwave frequencies. One side as a portion cut out so that you can pump more microwaves into the cavity. Of course, there is still significant loss, especially if you're cooking something
I suggest you take a look at howstuffworks.com, they should have lots of info on lasers, optical amplifiers, and microwaves