I have a Christmas Cactus that is literally falling apart branch by branch. Any ideas why?

Have you been watering it correctly? It's a cactus so overwatering it will cause it to rot. Has anyone else taken care of your plant recently? Maybe they were not following your pattern of care. I know you've taken care of it just fine for a couple of years but here is the recommended schedule:

The schedule of the ideal life of a Christmas Cactus

January - Flowering.

February to March - Resting (55 degrees, infrequent watering).

April to May - Water thoroughly when potting mix begins to dry out.

June to August - Place outdoors in a shady spot.

September to October - Plant prepares to flower. Reduce length daylight hours. Keep on the dry side and cool (55 to 60 degrees F) until flower buds form. Then increase water and temperature.

November to December - Flowering. Water normally. Temperature no less than 55 degrees F.

Xmas catus are very beautiful but equally sensitive plant. I have one too which automatically stopped flowering .Take the pot inside to a darker room. Keep it in this dark set up for 1 to 2 weeks .Mine started reflowering after i left it alone in the corner of my bedroom .I am seeing a few buds here and there now.The plant needs water but not too much water it twice a week for intial 2 weeks and then once a week after that. Get some cactus fertilizer or simple liquid fertilizer. I hate to let go off my plants how this helps all the best.

Too much light and too much watering can cause it to become more delicate. It should also not be too warm. Water once about every two weeks in winter or even less. It needs more water when actively flowering and growing. It could also need a bit of plant food. Water it and apply some plant food, then let it almost dry out before you give it a bit of water again. It should just be moist, but barely. Keep it in indirect light.

This is Easy! Air Force Army Navy Then Marines! Close behind Coast Gaurd.

I had a Christmas Cactus that became feeble. It responded really well to plant food. Your soil's nutrients have probably diwndled over time.

I have one too. Try putting it in a warmer climate. Or put it in a sunnier place! Also, try putting egg shells in the water, that helps a lot.