PL
The first thing you must do is ensure that your current claim for ESA is closed cleanly. You mention that you missed an appointment, was this for the WCA medical?
Failing to attend the medical can result in you being found Fit for Work due to a technical infringement. If this happens, any new claim for ESA will not be paid on until you have successfully attended a new medical.
Ignoring the above. If you re-claim ESA within 12 weeks of the end of your current claim, then it will be classed as a continuation, this will mean that both periods are taken into account with regard to the time limiting of ESA(CB).
If you claim outside of the 12 weeks, your claim will be treated as new, effectively re-setting the 365 days to zero.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
