Endure sixty seconds of the eleventh hour? (4-6)
I believe the answer is:
last-minute
'the eleventh hour?' is the definition.
(thesaurus)
'endure sixty seconds' is the wordplay.
'endure' becomes 'last' (synonyms).
'sixty seconds' becomes 'minute' (I've seen this before).
'last'+'minute'='LAST-MINUTE'
'of' acts as a link.
(Other definitions for last-minute that I've seen before include "Done at the final moment" , "very late" , "Eleventh-hour" , "Done at the latest possible moment" , "Eleventh hour" .)