Hello there and thanks for the extra information.
Skin diseases in dogs can be very frustrating to diagnose and treat, and often do require investigation as well as trial and error with respect to treatment too.
The good news is that although the patches of hair loss aren't attractive to look at, they are not bothering your dog so you and your vet have time to work through the problem logically.
The first thing to say is that it is quite uncommon to have patches of hair loss that are truly bald - very often dogs and cats groom the hair away because of an irritation or they rub the hair away, but if there is absolutley no hair in these areas then this suggests that there is a problem with the body actually making and producing the hair, rather than it being lost.
I would say first of all thought that it is vital that flea and worm contrl is kept up at all times with any case of skin trouble, even if parasites are not suspected as being the major cause, as even one bite from a flea on a sensitive dog can make a small problem very suddenly bigger!
If the antibiotics do not do any good, and I would be surprised if they do - then the next step would be for your vet to examine some scrapings of the skin and hair pluck too to see if there are any external parasites present. There is also chance here to see if any microscopic remains of hair are there too, and what they look like. This is the most basic of exams and really important to do, as there is no point getting bogged down in complicated stuff if there is a simple cause visible.
If this is all normal, then you are faced with the decision as to how much you do about this problem, given that the dog is not bothered by it at all. Cosmetic diseases can be frustrating, but if they are not affecting the general well being, then they do not always need treating. One thing that I would check for with a blood sample though is an underactive thyroid - which can cause certain patches of hair loss (usually on the flanks, not the legs though) in the dog and this can be the first sign. I think it is important to rule this out as the disease can go on to affect the dog in other ways later on.
Hormones can be guilty of causing hair loss too - and they can range from testosterone associated hair loss, again not a problem if you have an entire dog as long as they are fit and well and there is no sign of testicular pain or enlargement, to hair loss associated with the seasons. This is called seasonal alopecia and causes hair loss at certain times of year - leaving behind black patches of skin that are completely soft and bald and then these resolve as the day length changes with season. This disease is purely cosmetic and requires no treatment, and sometimes the only way to diagnose is to wait and see what grow in 6 months time!
If nothing appears to be giving you the answer and you are still concerned, and the thyroid is normal then the next step would be to have the dog sedated and actually take some biopsies of the normal and abnormal skin, and also the junction of the two to be examined by a pathologist. These guys can look at cross sections of the skin and see what the hair follicles are up to, whether there is hair being generated, whether there is inflammation in the skin etc. etc. and give a much clearer picture. Whether the disease is treatable, of even whether it needs treating again should become clearer. I think that it all boils down to whether the dog is otherwise happy and healthy, whether the disease appears to be progressing and getting worse, and how you feel about it as his owner.
In the world of dermatology, there is often no clear path, and no right and wrong way to go about things, but being logical is by far the easiest!