Our female Sheepdog went through something similar, but seems to have conquered it. Our inside stairs are slippery hard wood...no carpet. When she and her brother ran down FAST one time, her feet slipped all over the place and she sort of slid down the stairs. For about a month after that, she would go up the stairs without a problem, but would stand at the top and whimper. If we got her going a little, her back feet would begin to slie out sideways. I was holding her shoulders guiding her down the stairs as she slid on her stomach.
When I determined it was not physical...she walked, ran, jumped on the bed, etc., I figured it was psychological. Instead of taking her to a shrink, I did the most logical thing. I bribed her with bits of kibble at the bottom of the stairs. I urged her to come, and would say, "slowly...slowl y..." until she began to carefully take the steps one by one. She now does fine without the treats, but likes to stick close to the left wall. We're working on that now.
Once they slip or fall, they don't forget...excep t maybe treats will help them to forget.Good luck,
Nancy