Hello-
your post rang a bell in my (very old cogs of) my brain - I've just looked.
One poster thought her 2 pigs have been taken by a fox but the cage was still locked.
Another poster suggested it could be a wild mink. (I've never seen one but I wouldn't be able to tell)
Weasels (I googled) will eat birds and small mammels, so they could kill a small GP ,logically, especially if the GP couldn't escape.
We have foxes and cats in the garden, but if the pigs went into their hedgehog house they'd be sheltered, but only if the predator couldn't get into the run.
I googled rats and mice. I don't think they'd be a threat to the GP but could contaminate their food.
Could you re-inforce the chicken wire, double it up? If you go to a DIY shop they'll have different fencing and could advice.
My DH made our GP inner screen door with half wood (lower part) and an old fireguard (so small, tough wire rectangles) Clever DH and cost nothing.
When we were buying a run, alot of them were wood and chicken wire. I thought it looked a bit flimsy TBH.I bought a rabbit run that is metal/chrome ,with1" gaps (same size as your hutch wire)and long 'tent pegs' to pin it down. We leave it on the lawn and DH moves it when the grass looks exhausted.
I'd imagine a predator would get in if they could find a big enough gap in the mesh, so if you reinforce and check for damage regularly, the should be fine.
When I was a child, our GPs were free range at grazing time. There weren't foxes or dogs, but a few cats (they had their cages open with a secure area0
but we lived very near hills where there were adders! Luckily they didn't venture near people 