Losing sweetheart a danger this month (5)
I believe the answer is:
april
'this month' is the definition.
(April is an example)
'losing sweetheart a danger' is the wordplay.
'losing' indicates named letters should be taken away.
'sweetheart' becomes 'e' (the heart/centre of 'sweet').
'danger' becomes 'peril' (peril is a kind of danger).
'a'+'peril'='aperil'
'aperil' with 'e' taken away is 'APRIL'.
(Other definitions for april that I've seen before include "Month to be in England (Browning)" , "Thirty days in spring" , "period of time" , "'All in an ... evening' (Katharine Tynan)" , "on her first kid" .)