It flickers at the end of three months (5)
I believe the answer is:
ember
I believe this is a double definition.
'it flickers' is the first definition.
'the end of three months' is the second definition.
(September, November and December)
'at' acts as a link.
(Other definitions for ember that I've seen before include "Smouldering piece of dying fire" , "Material in dying fire" , "Small piece of glowing coal in a dying fire" , "Glowing cinder" , "Glowing coal; type of goose" .)