Mainly when I believe the outcome of the job will be so poor that the customer is better off replacing the carpet, furniture, or whatever I'm being asked to clean. If the customer understands both the final result of the job is not going to be perfect and that I may have to charge substantially more than normal to get it as good as possible I may go ahead and proceed. Some urine jobs are just so far gone that no matter what you do the job will just be a stop-gap to get the place cleaner until the owner can replace both carpet and pad.
I rejected cleaning a viscose rug because the wear was so significant that cleaning would not have improved the appearance in the slightest. I explained why the rug was in so bad a condition compared to her other synthetic rugs that looked great. If she still had wanted it cleaned I would have done it but asked for her to sign a waiver for my own protection. As we know these rugs are garbage, but some are quite expensive garbage!!! I am doing a tile job later this week where I explained the damage in her kitchen was fairly minor, but she still decided to replace the whole kitchen, utility, and 1 bathroom. I didn't refuse the job but wanted to be sure she would be satisfied with the final result and she OWNED the damage. I am doing the tile & grout that they are not replacing and they may yet change their minds.