Ah, that makes sense.
Do you lock the chickens in the coop at night?
More predator attacks happen at night than by day. So locking them in the coop will probably prevent more than 3/4 of possible predator issues.
The chickens really might be OK.
Is there usually someone home during the day...
Do you have a picture of the run, or a link to a website showing it?
Did it come with chainlink fencing?
Animals small enough to go through chainlink fencing are usually too weak to destroy chicken wire, so chainlink + chicken wire can be a pretty good combination.