I have an adorable 10 lb rescue mutt, who has been "housetrained" for awhile now (a year ish). We will, however, constantly have relapses... and I can never catch him!

He is kenneled when we are gone, but its when we are here that he has taken to peeing on clotheslines, edges of trashcans, etc. Turn your back for a second and there goes your clean laundry. We only have 650 square feet right now, so he really isn't unsupervised for any length of time. Every so often he will have several episodes of this, and then its back to being perfectly house trained. I wouldn't be quite so upset if he didn't so obviously lift his leg to catch the upper parts of my wall...

Is he even house broken, or have I done something wrong? Is he healthy? He is fixed, but could he be marking? HELP my carpet cannot take much more!

The first concern would be a medical issue, such as a urinary tract infection. To rule that out you'll have to see a vet.

You did mention a few things that raised some concerns. You stated that he's not supervise all the time.

A dog is a dog, and many people think that they should understand what's right and wrong. They don't. They have to be trained to live in our world. To a dog, peeing when you need to pee, in the space available, is acceptable, and normal.

Don't think that it's your fault, many dog owners make the mistake of thinking that their dogs know not to pee in the house.

Right now you have to be consistent. That means that you have to work for it. You need to take your dog outside, ask him to potty "choose a potty word, and stick with it at all times", and when he does, lots of praise, a treat, let him know he's a very good dog.

When he has an accident, don't yell, don't get mad, don't put his nose in his mess. That teaches him nothing. I'm not saying that that's what you're doing, but many owners make that mistake as well.

Just take him outside, give him the potty command, and wait for him to comply. If you catch him in the act, it's a firm "no!" and then right outside.

He has to learn what's acceptable, and he doesn't understand English, or the rules we humans live by. He has to be shown.

The more consistent you are, the more effort you put into this, the more reliable he'll be. :)