How Can I Prevent My Pets from Re-marking Carpet, Even After Shampooing ?

I had to hire a professional to clean the carpet for the marking to stop. Their product and machine did the trick. The urine gets through the carpet and into the padding...the pro-quality equipment can really get into the padding and get the smell out. I didn't expect it to work because I had cleaned with a Rug Doctor and the pet treatment products many times but was pleasantly surprised that after I had a guy come in and do a deep cleaning, the marking stopped.

I'd talk to a vet and/or dog trainer.
First make sure the dog doesn't have a health issue which might be coming out this way.
After he has a clean bill of health then see about addressing and retraining his behavior.
Your other options are to crate the dog (if he does this when no one is home), remove the carpet or keep the dog off the carpet - I know one family who only lets the dog in the kitchen or other un carpeted rooms.
Good luck!

After our cat had a UTI, we ended up having to remove the carpet and padding, plus we scrubbed and sealed the subfloor. Surface cleaning, even with a professional enzyme, wasn't enough to reach all the way down. Even when humans can't smell it the animals can.

Added: If your dogs have not been to the vet for testing, do that first.

Use vinegar in the carpet scrubber. Go or the area many times. The vinegar will take out the urine smell.

You need an enzyme cleaner that will break down the urine because while you don't smell it the animals still do. The one I found that really worked was Roxie and Roxie PROFESSIONAL STRENGTH STAIN & ODOR ELIMINATOR - ENZYME-POWERED PET ODOR & STAIN REMOVER FOR DOG AND CATS URINE which I got on amazon. Worked better than anything I got at the pet or grocery store. You spray it on, leave it sit for a couple hours and it usually takes care of it with one treatment.

You can also rearrange your thing so that the spot is covered for a while to get them out of the habit.