It sounds like you have a spider mite infestation. It can kill the plant, but it is very easy to control.  Spider mites locate on the under side of the leaves and can be eliminated by washing the plant with a strong stream of just plain water several days in a row to break the breeding cycle.  Once that is done, you should make it a habit to wash your plants at least once a week.  I have found that with roses that have dense foliage, it's a good idea to make sure I get at more than the easily reached foliage because an infestation can start on the foliage on the interior of the plant, too.

Some people are willing to engage in chemical warfare with these critters, but my own experience tells me  to take the conservative approach first and see if that solves the problem.  So far, I have never had to advance to a harsher treatment and cannot give you any advice along those lines.

You might want to click on the "Search Posts" on the Q & A Forum page, enter "spider mites" > "match phrase exactly" > "Search".  You'll find other posts written about this pest.

Smiles,

Lyn, helpmefind.com