Have you ever replaced the soil or thought of repotting. If you fertilize a lot, the soil may be full of salts from the fertilizer. Remove from pot and see if roots the shape of pot. If so put it in a slightly bigger pot. This looks like a 10" so go to 12", if it's a 12" go to 14" or 15". Put in 2" of compost on top of soil after planting. Oh, and break up or cut the roots on the bottom or they will stay in the same shape forever. If you disturb them they will grow out. Once it's in the new pot be careful to not over water. If you water once a week now, stretch it out to 10 days. The plant being in the small pot sucked up the water quickly, in a bigger pot their is more volume and more water to assimilate and it will be longer before it needs more water.

I'd guess that the lower parts of the plant are below the light-compensation level. Or maybe the plant sacrifices its lower leaves when it gets too dry. The pot is far too small for the size of the plant, which would tend to make the soil dry out too quickly. If I were you, I'd cut the stems way back to the points where they fork, replant the plant in a much larger pot with good planting mix, and try to place it where it gets more light from the side. I'd also add slow-release fertilizer to the soil.

it's outgrown the pot & it's probably rootbound.

remove it to a larger pot & freshen up the soil. tease out the roots.

Outgrowing the pot.

OK, please read this BEFORE giving the same-old-same-old answer.

My poinsettia is 2 1/2 years old. It is 4 1/2 feet tall. I let it grow to see how big it'd get.

So here's the thing:

I have about 5 long branches, and the leaves are turning yellow, drooping, and falling off at the bottom... The top 12 inches of each branch is doing great.

In other words, for 3 1/2 feet, there are no leaves (or they're falling off), and the top 12 inches is thriving.

I want this plant to do well; what should I do?