I don't know much about poinsettias, but this article on davesgarden has some care tips! There's more than one article on the site, just search "poinsettia" in the search bar. Davesgarden is a pretty good resource for plant care for any plant tbh, because if an article gets something wrong there WILL be people in the comments arguing about it lmao, and often comments on articles or on plant pages offer more insight. It's where I learned to first care for succulents.
Anyway, from the little research I just did, the most likely reason for your poinsettias "dying" is that they're actually deciduous plants and enter a period of dormancy right after Christmas, so they'll drop their leaves and flowers and look like they're dying but it's just like any deciduous tree shedding their leaves for winter. Also, in the wild they actually grow as small trees.
If you already know about dormancy and you're talking about your plants actually dying-dying, then another reason could be 1. they don't have enough drainage, 2. they're in the wrong soil. I'm grouping them together because they're both related to the potting medium. MOST LIKELY, the reason is drainage. Just repot them in a pot with drainage holes. I'm guessing if you just take off the fancy wrapper they're sold in, the pot that they came in probably will have drainage holes, they were just trapped by fancy wrapping paper. Poinsettias don't like too much water, and, much like orchids, they need adequate drainage. Too much sitting water in their pots = bad. They will rot.
And in terms of soil... I've mentioned before that most potting soil is actually peat, but their natural environment is in dry tropical forests in mexico, clinging to sheer cliff faces. Think the walls of the Grand Canyon. Because I always go Too Deep with these things, I found the original paper that used genetic sequencing to trace cultivated poinsettias to a specific population in Northern Guerrero, Mexico. Which, btw, is actually an outlier in terms of wild poinsettia populations, because that region is much further inland. Most wild poinsettias grow on the coast. Anyway. I'm getting sidetracked. What I mean to say is: their wild environment is not in wetlands, which peat is great at mimicking, because peat is made in wetlands. Normal potting soil might be too dense + hold too much water, especially if you live in a humid environment. They like being consistently moist, but they hate being wet.
Luckily, this is easy to fix. Just get a bag of perlite (look up gardening centres/greenhouses near you if you don't know where to get perlite) and mix some in with your soil. You can mix in compost and sand if you want to get fancy but that's for the people who like making their own dirt. If you're like "that is way too complicated", congrats on being normal, and also, just get the perlite. The rest is unnecessary.
Though, tbh, with adequate drainage I doubt you'll even need to add perlite? Peat is pretty good at "moist, but not soggy" as long as it's not waterlogged. If you water your plants with a saucer under the pot, dump out the extra water after 10 minutes, or water from the bottom. But, again, the most likely reason is that your plant is just going dormant. Leave them alone until mid spring and give them less water than usual and they should perk back up :) April is when leaves start coming back I think? But don't quote me on this. I know April and August are the best months to prune them, and spring pruning is usually timed when trees and shrubs first start budding, so.
