Many people don't realize that training is an ongoing forever thing. You don't just train and the dog remembers. The dog remembers as long as training is reinforced every single day. If the dog doesn' ASK to go out, you take him out anyway. If at all possible, a good schedule would be a 45 minute walk every early morning, a comfort walk at11am, a comfort walk at 4pm and one last long walk (no less than 1/2 hour) before 9 pm. It is also a good idea to take different routes and not do the same walk day in and day out.
In answer to the other part of your question, an unneutered male WILL mark more than a neutered male. But if your dog has been doing this for as long as you say, it is also an ingrained habit and probably some sort of emotional release as well. So neutering now will probably help, but don't forget that training is necessary too...you may have to really be on this for a while to catch him as he starts to mark..and stop him. You will get to recognize the signs,...circling, sniffing,starting to squat or lift his leg...and you stop him right there and take him out.
It is not as easy a solution as just neutering...need to train too.