Clutch them when all looks lost, but avoid the short one! (6)
I believe the answer is:
straws
This clue is a double definition.
'clutch them when all looks lost' is the first definition.
(as in clutching at straws)
'avoid the short one' is the second definition.
(as in 'the last straw')
'but' is the link.
(Other definitions for straws that I've seen before include "are drawn thusto drink!" , "Thin tubes to suck up liquid" , "Tubes used to suck liquids" , "Thin plastic or paper tubes" , "Dried grain stalks" .)