Yeah... cutting on the vines really takes a toll on them... If the deer don't find them, and you haven't chopped them... Much better off all the way around.
Or... enclose a wider area in deer fencing.
I find that running the fencing along the woodland edge or among the shrubbery plantings is better than across open areas...
You need a 10 foot fence when running across an open mowed area, vs a 5 foot fence when run through the thicket... And... 10 ft may still get jumped!
Kinda surprised at how often someone around here puts up a deer fence and then "maintains" fence by spraying foliage with roundup...
That just isn't going to work!
Edit:
Re: chicken wire...
In my experience... not the best garden fencing... doesn't take very long to degrade to where they just walk through it like it isn't there...
I like the welded wire...
(pic from home depot website)