We go down, ultimately, for a very long time (3)
I believe the answer is:
eon
'very long time' is the definition.
(an extremely long period of time)
'we go down ultimately' is the wordplay.
'ultimately' says to take the final letters.
The last letters of 'we go down' are 'EON'.
'for a' is the link.
(Other definitions for eon that I've seen before include "plenty of time" , "Era" , "Major division of geological time" , "In time, long division" , "An immense time" .)