Lack of humidity is probably the cause of the leaf loss and dying buds over the winter, but see below. At this point, it's obviously alive, so there is hope. Now about the braiding... Is it three separate intertwined plants or a single plant with three main stems woven together? In either case, it does seem to me that either the braided parts will cut off each other's ability to move water and nutrients or they will unite into a single stem just as if they had been grafted together. Can you tell if leaves are emerging from all three stems? If one or more is leafless, it/they may already be dead and can be cut out. You will wind up with something that does not look much like what you first received, but it will be able to live and grow.

Thanks! The humidity issue sounds relevant because it did appear that the leaves just dried up, no obvious sign of disease. Also I neglected to water it during a vacation which may have exacerbated things. Actually there appear to me to be 4 stems. All 4 stems have leaves and none seems to be doing much better than the others in terms of leafing out. Also it appears that the 4 stems are emerging from at least 3 separate plants at the base. Perhaps it started out as 4 stems and now 2 of them appear as though they have been grafted together as you say. I am wondering if I should re-pot it and if so at what season and with any particular soil requirements? Also at what point should I apply fertilizer and what type?

Four stems it is. Stems or even tree trunks which are braided in this way do often unite at the point of contact. It was once a faiirly common practice to create such braids for a unique garden feature.

You can repot at any time. Use a soil-less planting mix which provides good drainage and is suitable for acid soil plants. A garden center should be able to supply what you need. Use a pot only slightly larger than the one it's in so that it does not remain overly wet. Peat based planting mixes usually contain no fertilizer. It's best to avoid the ones that do. Instead, use controlled release fertilizer following the directions for the quantity. With no fertilizer for a year, your azalea may cheer at the sight of the container.

Ok thanks! I will do that. I think you may have helped me in the past too. I also have 3 evergreen rhododendrons and I think you helped me decide where to place them and how to protect them. In any event every winter I am absolutely sure they have died, the leaves are so incredibly wilted, and then every spring they are still blooming nice enough for me. I think it has been at least 5 years. They don't appear to be growing hardly at all, but most of the wilted leaves seem to recover, and also new leaves come out to replace old ones, and enough blooms every year to keep me happy. When I got the rhododendrons, I mistakenly thought they would look nice in the winter, which they certainly do not in my climate, but spring makes up for that. In any event, it is amusing for me to see that an azalea will also play dead, and yet as I examine it again today, I am encouraged by your comments and also by its appearance, that it can make a good recovery, so I am eager to try repotting now. Thanks!

You are very welcome. The name for the technique of deliberately entwining living plants so that they unite just would not come to me until this morning. The term is "pleaching" and it has a very long history. Pleached trees, usually apples or other fruit, are clearly visible in a number of Medieval manuscripts and Books of Hours. Remembering the term led me to check on a nursery I had not heard of in 40 years or so. To my amazement, the Leuthhardt Nursery on Long Island is still in business after 80+ years and still producing espaliered fruit trees some of which are designed to become pleached as they grow. So thanks to your original inquiry, I had a good memory jog and gained the fascinating tidbit that the ancient arts of espalier and pleaching live on.