How old is your puppy? Mine started walking down and up the stairs when he reached 10 weeks old. many others had done the same and have not had any problems. be careful, do not push him to walk unless he does by himself without any problems.
Too many stairs too often *can* cause problems for puppies, but it isn't something that can never be done. I think one of the bigger fears is a pup jumping down a lot of stairs at once and hurting itself. Or taking a tumble and being fearful of stairs because of it.