yes squirrels have done this in my garden to a range of plants. grrr

Are you sure it is an animal or a bite? How cleanly cut are the stems? It seems too tall up the plants for rabbits or other animals. We once had all our runner beans eaten near the base by geese, for which I initially blamed slugs.
Could it be two legged creatures in this case, armed with scissors? Might strike a couple of bored little boys as an amusing thing to do?

Well I guess squirrels are two legged creatures, sort of, but probably not armed with scissors, though you can never trust a grey squirrel!
(We posted at the same time, Seaburngirl)

I have had a similar thing with my pumpkin vines. Mine where 'snapped' near the base though, not a high up as yours. Lost three vines this way. Found the tops next to the base which was left in the ground, almost as if someone has snapped it right off. The forth and last vine, I popped a cloche over it and that one lasted a while until I looked closer the other day and found that had been snapped too. (They were all out of reach in an enclosed garden). Last year I grew pumpkins sucessfully. This year we will have none! The only thing I could think of was either that the wood pigeons have done it??????? They hang about around that area of the garden daily, or slugs. However, it was not obviously slugs as there was no damage to the leaf, I had just found a few slug trails in that area.

SO, i'd be interested to know the answer to your question too.

Thats interesting Bertiefox, as we get a lot of grey squirrels in our garden, they usually eat the bird seed in the trees (as you can see from my profile picture!) Little blighters, I didn't think of that!

Thanks for all your responses so far. It's very interesting that others have experienced the same kind of thing. Whatever it is, it's intriguing that they haven't actually eaten anything. Just bitten the stems in two (I'm resisting saying snipped at the moment!). Is it possible that they are very intelligently attempting to fell the plant, but don't quite have the intelligence to realise that it's attached higher up?