How is the energy of an electron lost in a classical hydrogen atom?

Consider the following.
You have an electron of negative charge orbiting a proton of positive charge at some distance R (i.e. a classical hydrogen atom).

I understand the hydrogen atom is unstable under classical physics because the accelerating electron loses its kinetic energy as electromagnetic radiation.

My question is set up as follows.
All you have is the proton acting on the electron.
In the rest frame of the proton, the electric field is constant, extending radially outward, so that it can do no work on the electron,
In the rest frame of the proton, there is no magnetic field on the electron due to the proton either.

What field is slowing down the electron?

Any comments would be appreciated, as this has puzzled me for quite come time.

Source: http://www.physicsforums.com/showthread.php?t=701952&goto=newpost

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