Assuming you are unscrewing the right way (conventional thread, go anti-clockwise on the ring), then it may just need some more welly. The rings are not smooth, they have ridges underneath that stop them vibrating loose, so it can take a bit of effort to get them to move.
The worst I've had was when I'd let a guy at Halfords replace the wheel bearings for me. (Actually, I was very grateful to him - I was in Shrewsbury having ridden up from Basingstoke that morning, it was January, snowing, and I had to get to Bangor that evening. The bearings had gone really, really noisy about 15 miles before Shrewsbury. He dropped everything and fixed it for me). He'd cranked the lockring up really tight, I needed a hammer tap on the lockring tool to free it up.