That good care might actually be the problem, if it includes daily watering. Granted, a potbound plant may dry out quickly and require a daily douse. If yours stays wilted even when its soil is damp, however, you've probably been overgenerous with the watering can.
That stagnant moisture building up in the soil eventually gets invaded by one of several fungi which can rot the plant's roots. (The one pictured to the left here is pythium.) Without those roots to draw up moisture, the plant eventually dies of thirst in soggy soil. Since most of the drama is happening beneath the soil surface, the collapse can appear sudden, though there may be some discoloring or dropping of leaves first. Although the plant in the thumbnail was actually just wilted from underwatering, its droop looks very similar to that caused by root rot.
There are some species, of course, that wouldn't mind standing in water permanently. Papyrus comes to mind! Rooted cuttings frequently survive ankle-deep in H2O on my windowsill for weeks too. I suspect the fact that the cuttings' roots get light--through the sides of their glass jelly jars--might be a saving factor there.
Root rot does seem more prevalent during the winter, probably because plants don't get as much sun and warmth then, and cold, damp soil exacerbates the problem. Potted citrus trees are notoriously prone to succumb, so be very careful if you have those.
Keep a wary eye on moth orchids (Phalaenopsis types) too. I only water mine every three days or so, but even that turns out to be too much sometimes. Those orchids are often potted in moss when they come from the store. Over time that medium begins to break down and retain more water than it did originally. I've found that the surface of the moss can look dry, when it is actually rotting underneath.
That breakdown can happen with the wood chip orchid medium too, though it usually takes longer. Problems are most likely to develop when the orchids came with cache pots--outer pots without drainage holes. Removing the orchids' inner pots from the cache pots helps, but it's still best to watch for signs of trouble. Note, in the photos here, how the orchid's leaves appear to have deep wrinkles in them. The leaves on healthy plants should be much more succulent.
Speaking of which, orchids aren't the only succulents that can rot easily. One of my other losses was a wax begonia I'd had for years. It boasted unusual tri-colored flowers, which you can see pictured to the left here. As it had grown to fill a large pot, I usually watered it every day. One autumn when I didn't have much room under the growlights, I positioned the begonia at the dim end, thinking it could survive anything. Out of habit, however, I kept watering it every day. You can guess what happened there--a sudden collapse.
Most rot-prone plants should probably be in clay pots, as moisture can evaporate through the sides of those. In my experience, even glazed ceramic pots work better for succulents than plastic. But what can you do about plants that are already drooping?
By the time they wilt, they are pretty far gone, but emergency measures will sometimes save them. You have to cut off all the infected roots first, of course. They will be the black or dark brown, decayed-looking ones, as healthy roots are generally cream-colored or light tan. You can see, in the photos, how drastically the orchid photographer had to trim those on her phalaenopsis.
People on citrus forums frequently recommend dunking any good roots that remain in a bleach and water mixture--usually about one part bleach to nine parts water. Although I haven't tried this, I have immersed aquarium plants very briefly in a more diluted bleach solution without it causing them any harm.
I would only soak those roots for a few seconds, however, and rinse them off immediately afterwards. I would then prune the top of the plant back until it's short enough for the remaining roots to support it, and put it in fresh potting soil or bark in a smaller new pot. For types which rot easily--other than orchids--you should probably opt for the cactus and citrus type of potting soil.
If bleach sounds too scary, you might want to try another fungicide instead. Setting the pot on a seedling heat mat while the plant recovers might help as well.
I frequently give the vitamin and hormone supplement SuperthriveTM to sick or stressed plants too, but you will want to avoid actual fertilizer until they recover. Most shouldn't be fertilized during the winter anyhow.
For the more vulnerable types, it's a good idea to stick a finger into the soil or other potting medium occasionally to make sure it isn't sopping beneath the surface. Occasionally I make the opposite mistake and don't water a plant because its soil appears wet. I've found out the hard way that some soils can look dark when they are bone dry!
Photos: The thumbnail photo is by Amy Templeman, the pythium root rot photo by Scott Nelson, and the orchid photos by Maja Dumat, all courtesy of Flickr Creative Commons. The begonia photo is mine.