  de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen
problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003
simulations support the stability, our recent numerics always lead to
self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic
orbits. For very eccentric orbits with energy close to zero and angular
momentum below some not-small value, there is on the average a net gain in
energy for each revolution, which explains the self-ionisation. Next, an
$1/r^2$ potential is added, which could stem from a dipolar deformation of the
nuclear charge by the electron at its moving position. This shape retains the
analytical solvability. When it is enough repulsive, the ground state of this
modified hydrogen problem is predicted to be stable. The same conclusions hold
for positronium.
