Why do you think it looks sickly?
Don't over water....they want to be on the dry side. And to control bloom give it lots of natural light and as little artificial as possible. Bloom time is controlled by day length.

you better quiz mom .. and follow HER DIRECTIONS precisely .. and dont screw it all up by thinking you can do it better ...

crikey.. shes been doing it for 50 years ... what more can we add???

the first thing i would do.. is start a couple more plants .. to insure that if i mess one up ... i will have backups ...

and dont forget.. if you move it to a new home.. that will be a giant stress .. and you need to perfect placement before your do anything else ...

a pic would help

ken

https://duckduckgo.com/?q=Christmas+Cactus+propagation&t=ffcm&iax=videos&ia=videos

photo? CC droops, so without seeing the good, clear photo it is hard to tell...has it ever been repotted? Such old plants are often in the same pot for years.

Definitely need to see pics, especially of the type of potting mix being used.

And, as Ken said, root some cuttings to ensure (in the worst case scenario) that some of this heirloom plant survives. I have done the same with my oldest Christmas Cactus, which is now over 40 years old.

Christmas Cactus are Brazillian jungle cacti that are rained on nearly every day, and they should not be kept dry - the mix should be barky, porous, free draining, and should remain uniformly moist for maximum vitality.

If the plant hasn't been pruned in quite a while, pruning back the branches will create new growth and budsites where future blooms will occur. Similarly, if it hasn't been repotted or fertilized in a while, this, too, will increase its vitality.

Mine still had a few lingering blooms in mid-March.