I continued to lose weight, very slowly, for much longer than that. When I got to within 5-10 lbs of my goal, though, I did start counting calories, and that made it much easier to lose the rest.
I do know many people here object to counting calories, but if you ever get stuck for a long time, and you're willing, it's worth a shot. If you're only in your second month, I wouldn't think you'd be at that stage yet though. And in general, I think the slower you lose, the better, although it's hard to be patient.
My skin showed improvement very slowly. I had eczema too, as well as keratosis pilaris. Both are 95% gone now, but I think that took almost a year, and I don't know that paleo per se was the "cure", so much as eating a diet much higher in saturated fat and improving my omega 3/omega 6 balance & K2 intake, and probably my general vitamin/mineral intake in general.