An electron's "standard orbit" is a non-changing situation, so the electron has constant Potential Energy, and constant Kinetic Energy (hence constant momentum and constant wavelength).
1) If an electron DID absorb Energy (from a photon, for example), its total Energy would be changed (PE increases toward zero, and KE decreases ½ as far toward zero), which would be called a "transition" from initial state (orbit n1) to higher final state (orbit n2).
2) If you were asking why the electron doesn't radiate during its "circular Bohr orbit" (which has centripetal acceleration), the answer is that the electron's wavelength "fits" along its path so that it reinforces itself (constructive interference). Because there is no change in the Electric field, and no change in the Magnetic field, there is nothing to start EM radiation: so no Energy is emitted.
... it is the changing E-field and changing B-field, which become EM radiation from an accelerated charge ... the radiation is NOT deducible from Energy conservation
contrary to Zz's wording in the FAQ post ... it should be obvious that you can't derive a pair of vector fields {E(r), B(r)} from a single scalar equation.