It IS possible that it is something in your home or the dogs environment that is causing this continued problem. Allergic reactions begin with the first contact with the allergen. The first contact will most often produce no symptoms. subsequent contact will produce gradually worsening symptoms with each contact. There must be some allergen causing this problem. When treated the symptoms are ameliorated. Once treatment stops the allergen causes the reoccurrence of symptoms. You really have only two options. Remove the allergen from contact with the dog or continue treatment indefinitely. Consider insecticides, deodorants, pollens, plants, soaps and cleaning agents. I hope you can find a solution. Search for a vet who specializes in allergies.
I agree that allergies can take some time to develop - I would think more about what may be causing the problem. I would also want to be very sure that the vets have investigated for ingrowing lashes/hairs, blocked tear ducts, or anything else that may be causing inflammation. Is he still teething? That can cause weepy eyes, and if he is prone to showing his nictitating membrane it could be exacerbating it.
What month did it start? Was it unusually hot/cold/humid? What was in flower - trees, grasses, flowers? Did anything at all change in terms of cleaning, decorating, furnishings, perfume, soap, etc, etc? What can you cut out - enzyme washing powders, spray cleaners (try white vinegar instead), spray polish, air fresheners, etc may all cause problems. A member here recently realised that her dog's long standing stomach problems were caused by the canine dental paste she was using - tiny things can have big effects.
I hope you find the cause and a solution - the repeated infections would worry me, too.
Can you possible have your pups eyes checked by an optomologist? This could determine whether there is an actual eye problem, if there is not then you would pretty much know its allergies. I think average vets don't initially want to send you for expensive tests and will look at allergy symptoms if nothing is obvious to them.
Many of my poodles and nonpoodles have had seasonal allergies. Pollen and human dander (!!!) are common allergens for dogs. Sneezing, drippy eyes, and face rubbing were the usual symptoms. My dogs have always done well with cheap OTC antihistamines.
Two of my poodles have also had fluff around the eyes that causes irritation while the other two had hair that didn't seem so determined to get into their eyes. The trick there has been to keep all the excess foliage cropped back out of the way. I also flush eyes with sterile "artificial tears" after trimming faces.
The pollen count in the Northern UK has been sky high of late, as I know only too well. I would ask your vet about using a children's anti-histamine syrup if he is going to need a lot of it - check that it does not contain xylitol, of course, but it may be an economical way to buy exactly the same active ingredients, and can be given with a syringe to get the right dosage.
I leaned a tip from a much older person than I who would not be alive today. with eye problems "use cold black tea as an eye wash twice a day" It has worked for me with many dogs over time and is worth a try.
Just seeing them and them being slightly red is not an issue per se. I would invest the time to go see a veterinary ophthalmologist - they are the only ones who can truly tell if it is an issue or not. My Dalmatian had very prominent 3rd eyelids all his life - completely normal and not irritated although they looked pinkish-redish. Will attach pic so you can see.
My poodle does the same. More so in the right eye. He's been checked by my vet that said allergies. Zyrtec and Claritin did nothing to resolve the problem. I took Opie to a AKC show where there was a ophthalmologist checking eyes. She dilated eyes and didn't see any abnormalities but suggested he have a tear production test and may need his tear ducts flushed. She was not able to do the testing at the show. She was from the University of Tenn. I am getting Opie checked again this Thursday by another vet and may have to go to UT if she doesn't find anything. Opie's eyes clear up when I use a very warm wash towel and clean his face and hold the it to his eye for a some time. And sometimes they are clear on their own. I have researched and researched. The only other thing I can maybe think it is would be distichiasis. You can look this up.