I would cut out that little bud and start from there if it were my plants. Make sure the bud is very cleaned and callous well before rooting it. It is likely a fungus issue, you should also treat the bud with systemic fungicide once rooted to prevent spreading. The old plant is a gonner and it will eventually spread to the bud if left as is.

I'd say some remedial education is in order if you 'know how to take care of it' but it's looking like this. Your plant, as Alain explains, needs to start over with that one little offset. In the meantime, the soil you use should be altered so that the plant has a better chance of living once the pup is rooted. There are lots of soil discussions here - you can find one that you can make/purchase from available materials in your area.

That little bud grew where a much larger bud was which I removed about 3 weeks ago and potted separately after letting it cure for several days.

I have a opuntia that is doing very well and grown under the same conditions as the cereus. I even had to take cuttings from the opuntia because it was becoming unwieldy.

Deb,

Opuntia are a different kettle of fish than the rest of the cactus family - they'll grow under difficult conditions much more easily than their cereoid cousins and you can get away with a lot more ill-advised culture with them and not have a problem. I think what you have is an Opuntia that's in the Consolea subtribe. The more room you give it, the more it will grow, so it's a good idea to keep it contained in the pot that you have it in.