Electrons in a shell absorb energy and move to higher energy levels, but they release their energy and jump back to the shell they originally were in. Why do they jump back? Why can they not keep revolving around the nucleus?
This is a very fundamental question and for really understanding the "why" some advanced physics is involved. I will describe the process rather superficially.
As you might know, the level energies of atoms and molecules can be calculated (in principle) using quantum mechanics. The simplest system is the hydrogen atom as it consists of a single proton and a single electron. Ignoring higher order effects (such as interactions of electron and nuclear spins and QED effects), the quantum mechanical calculation gives the same result as the Bohr model, that is, the level energies of hydrogen are given by the Balmer formula, which you probably know.
The calculation does not predict that the excited levels fall back to the ground state. An electron in an excited orbital will, according to this calculation, always stay in this orbital if nothing happens to the system.
Because we know that excited states decay, something must happen to the system to induce the decay. It turns out that in our calculation we have ignored the interaction of the atom with the photon field. Atoms can absorb light and emit light and we have completely neglected this. If you do take this coupling into account, you will find that excited states have a limited lifetime and that an excited electron will fall back to a lower level eventually.
Many things are only stable in their lowest energy state: electrons are no different
Hold a ball in your hand. It is, in effect, in an excited state. Open your hand and the ball falls to the floor, without much effort or any push. Set the ball on the floor and it doesn't move. It is in its lowest energy state and won't move around unless given a push.
Many things are like that in the world. A cone is stable resting on its base. But resting on its tip, the very slightest fluctuation will cause it to fall over. This is a little like an electron being in an excited state, as is the case with a ball.
An electron in a high energy state is (to leave out a whole bunch of complicated quantum stuff) like the cone or the ball. Mostly, the slightest nudge it gets will cause it to fall to the state where it can exist at the lowest possible energy level.
There is a general heuristic in quantum physics, often referred to jokingly as the totalitarian principle, that everything not forbidden is compulsory. That is, any process that can occur will occur, with some rate, probability, or cross-section, provided that it doesn't violate any conservation laws.
An atom in an excited state can in most cases emit a photon without violating any conservation laws. (There are states like the 2s state of hydrogen that can't decay by emission of a single E1 photon because of conservation of parity.) Therefore we expect that this process will occur at some rate.