Given as this is a suddenly new problem for your blind and deaf dog, I wouldn't want to assume it was a picking up scent issue without first ruling out a urinary tract infection. You'll want your vet to run a urinalysis on a fresh urine sample to make sure all is ok. f not, she can get started on treatment to help clear this up. If all is ok, you'll want to pick up an enzymatic pet urine odor remover to use on the rug. Your vet likely will sell some or you can also get them at most pet supply stores. I personally like Pet Stain-Off, but there are quite a few to choose from. "Reminding" her where to go with a gentle leash walk off the porch for the next few days may help as well.
Best of luck, and let me know if i can help further.
Christine
Certified Veterinary Technician
Licensed veterinary technician (B.S. Mercy College), 10 yrs in animal medicine and training