My Grandparents had an issue like this once. Gramps put 4" diameter steel tubing into the ground, 4' under, 2' above, spaced 8' apart. Put half round anchors on each tube and hung chain made of 5/8" wire diameter between the posts, then filled the posts with concrete.
That was 30 years ago. They have since passed on, we've sold the house and its been through several different owners, but that fence is still intact and hasn't moved.