One of the main reasons for the failure of the Rutherford model of atomic structure, it is famously stated, is that the electron undergoing circular orbit loses energy since due to its centripetal acceleration. In the same line of thought, an electron undergoing uniform circular motion due to a perpendicular magnetic field must also lose energy, thus collapsing on its center of rotation. However, this is rarely the case (at least textbooks don't mention them). The electron continues the same motion undefinitely.
Can anyone please clarify the reason why energy is lost in the first case and not in the second?