It is shown that the total energy of the static ``field + particle'' system, defined in the framework of classical, renormalised electrodynamics of particles and fields, depends in an unstable way upon the field boundary data. It is argued that this phenomenon may be also an origin of the unstable dynamical behaviour of the system (i.e. existence of ``runaway solutions''). It is proved that a suitable polarisation mechanism of the particle restores the stability, at least on the level of statics. Whether or not it restores also the full, dynamical stability of the theory is still an open question.

PACS numbers: 41.20.Cv, 03.50.De