Dying remains end in three months (5)
I believe the answer is:
ember
I believe this is a double definition.
'dying remains' is the first definition.
'end in three months' is the second definition.
(end of September, November and December)
(Other definitions for ember that I've seen before include "Glower" , "Still smouldering fragment of wood or coal" , "Remnant of bonfire" , "Smouldering piece of dying fire" , "showing residual fire" .)