Second husband's deserted three times (5)
I believe the answer is:
trice
'second husband's' is the definition.
'trice' can be an answer for 'second' (both can mean a very short amount of time). I am not sure about the 'husband's' bit.
'deserted three times' is the wordplay.
'deserted' suggests removing the centre.
'three' becomes 'ter' (see Chambers).
'times' becomes 'ice' (I can't explain this - if you can you should give a lot more credence to this answer).
'ter' with its centre removed is 'tr'.
'tr'+'ice'='TRICE'
Can you help me to learn more?
(Other definitions for trice that I've seen before include "Very short moment" , "Flash" , "Haul" , "Next to no time" , "Very brief moment" .)