|MadSci Network: Chemistry|
The forces on an electron are the Coulombic repulsion from other electrons and attraction to the nucleus of the atom. In addition, the weak force is involved to some extent (see below).
Classical, i.e. non-quantum, physics does indeed predict that an electron moving around the nucleus "ought to" radiate energy and end up in the nucleus. However, we observe that this does not happen, with the rare exception of reverse beta decay in certain radioactive atoms (this is the case where the weak force is also involved). So, yes, in almost all cases an atom is "eternal" unless some external influence impinges on it (an energetic enough photon can knock an electron out of the atom, for instance, resulting in a free electron and an ion).
Instead, we observe that each electron settles into essentially a standing wave pattern around the nucleus. We call these "orbitals" but you must get out of your head any idea that a small, solid electron is whizzing around the nucleus in an elliptical orbit. Instead, the electron is "smeared out" over space, and the orbital is the spatial map of the probability of where it might be found at any given moment. This appears to be the way the Universe orders itself; we know the "how" that happens, but the deeper question of "why" it must be that way is, so far as I know, unanswered.
Atomic orbitals are a part of the study of quantum mechanics, a subject that will be somewhat difficult to approach at your grade level as it requires the use of differential equations. However, with some help from your science instructors at school, you should be able to work through enough of an introductory quantum mechanics textbook, such as "Quantum Physics" by Gasiorowicz, to get an idea of the basic concepts.
Try the links in the MadSci Library for more information on Chemistry.