Demand is breaking this month (6)
I believe the answer is:
insist
'demand' is the definition.
(to insist on something is to demand it)
'is breaking this month' is the wordplay.
'breaking' means one lot of letters goes inside another.
'this month' becomes 'inst' (letter-writing abbreviation for this month).
'is' going into 'inst' is 'INSIST'.
(Other definitions for insist that I've seen before include "Refuse to give way" , "Put one's foot down" , "Maintain firmly" , "Assert firmly" , "Demand firmly" .)