To AwesomeAlison:
1. You indicated that previous urinalysis tests have shown 'some bacteria' but 'not enough to qualify as a UTI.' I'd seriously question the intelligence of a Vet who is aware that this kind of problem has been going on for a whole year but didn't have the common sense to obtain a sterile urine sample and send off for a urine culture. That's gross negligence, IMO. NO bacteria should be present; urine is considered a sterile body fluid. I'd be going to current clinic; requesting a copy of all of kitty's vet records (this is totally your right to request this; just tell them that because problem has been going on x 1 yr, you want to look back at all records, for your own knowledge. Most of us request copies of our cats' lab/urine test results and keep them on file. Then I'd advise you to find a reputable Vet in the area (would be ideal if you could find a vet clinic that is a cat-only clinic) and take kitty there, with all past records for him/her to review. I'd request a new urinalysis be done......a sterile sample obtain by cystocentesis (they just insert a very very fine needle through abdomen into kitty's bladder and obtain urine that way)...then run a full proper urinalysis AND a urine culture/sensitivity.
2. A culture/sensitive (aka C&S) is the only way to truly identify the TYPE of bacteria present (there are many, many different types).....and then they test this bacteria with various different antibiotics to see which ones are 'resistant' to that type. It takes 72 hrs for the bacteria, if present, to grow on the agar plate. If there's a ton of bacteria, it can show as quickly as 24 hrs but usually they wait 48-72 hrs. If kitty's issue IS a UTI, Clavamox may not have been the correct antibiotic for the particular type of bacteria. and you say a 2nd type of antibiotic was used; a one-shot antibiotic that worked for 10 days. I suspect you're referring to Convenia (which actually works for 14 days).....and that one is really not recommended for UTIs; it's intended for the use of certain types of bacteria present in soft tissue, not common bacteria that cause UTIs.
3. Does kitty pee ANYWHERE else in the home? Or just this spot in front of the litterbox? How big is this cat? Is it at all possible that, like some cats, he's long in stature and he sort of miscalculates where he's standing in the box and his butt area ends up hanging over the edge of the box when he pees? If so, I'd recommend you try a much larger/longer litterbox I myself prefer to use those clear Rubbermaid storage containers; can get them cheaply at places like Walmart. they generally come with a lid, I just throw the lid away. They're a good 5 inches deep and much wider and longer than even an XL litterbox.
4. How long have you had the litterboxes you have? They should be completely tossed out after a year because despite how meticulous we keep them, urine inevitably can make it's way to the bottom of the box and plastic holds bacteria and odor (might not be odor humans can smell but cats can). Because I use the above Rubbermaid containers, they're very affordable to replace each year. I've gotten them on sale for like $12.
5. You might also try replacing the box that he pees beside with a hooded box...........these ones are "higher up the sides" so harder for a cat to have their butt hanging over the edge when doing their business but personally I'd try to Rubbermaid container first.
6. Kitty should be having xrays of bladder, to check for bladder stones that can cause discomfort AND blood in the urine (due to the inflammation of the lining of the bladder) and an ultrasound of the bladder - to check for any abnormalities with the bladder (kidneys, etc). Eg) if there's inflammation there, the U/S could show some thickening.
7. If the product that was used to clean the area when the carpet was steam-cleaned was some product that the steam-cleaning company endorses as 'able to completely remove pet urine', I'd try something else, like Nature's Miracle or Simple Solution; can get these at pet supply stores. I had my carpets steam cleaned a few months ago, prompted mostly by my finding my new adoptee having peed on a pile of clean laundry and a bath mat and I was terrified she'd peed in other places. The company told me they had some type of 'sanitizer' they could spray on the carpet to completely rid any cat urine. When i asked for more info on it, did it contain enzymes...they couldn't tell me much so I somehow doubt what they spray is as good as Nature's Miracle. In fact, all the guy did was walk around and spray it on the carpet surface. To clean cat urine properly, you have to totally saturate the area (including underpad) with the proper product. So based on this, I'm very "leary" of carpet cleaning companies who claim they have products to properly clean pet urine.