OP here: I have tried numerous things and I thought I would post an update.
First of all, my cat has no UTI and his kidney levels are actually improving due to the new rx food. So their recommendation was to put him on an antidepressant.

That just cracked me up! Does anyone else find it funny that my cat needs prozac??
Ok here is what I've tried:
I tried the vinegar/water combo and then sprinkled baking soda. Unfortunately that did not work. The smell came back.
The next thing I did was to split the spot into 3 equal parts and I tried 3 different products to see which one works the best. Here is what I found:
Nature's Miracle Orange Oxy Power--I thought this was going to work, but as it dries I can still smell a faint smell of pee coming through.
Petzyme Cleaner--This was the least effective. I still really smell the cat pee smell after trying this. This will definitely be going back.
Simple Solution Odor and Stain Remover--I think this one worked the best. I bought a big jug and I plan to try treating the entire spot with this one as well as some other older spots.
I'll keep you posted. I think I may have found another solution as well. I tried it in the upstairs where he went a few weeks ago and it smells pretty good up there. Here is the recipe I used:
1 Quart hot water
1/4 oxy clean
1/4 cup Tide powder (I used liquid as that was all I had)
1/3 cup white vinegar
Mix together in a spray bottle. Shake vigorously. Apply generously to the carpet. Use a scrub brush to really work into the fibers.
I let it dry a bit and then sprinkled some 20 Mule Borax on top. Once that dried I vacuumed it up.
This seemed to work upstairs pretty well. The thing is that upstairs is much more dry so it is hard to tell. The basement stays humid and so the smell keeps coming back.
If the Simple Solution doesn't work in the basement, I'm going to try the above recipe. I'm a woman on a mission!! Check out the photo in my signature.
Jen