They are hard to keep - I would like to find a person, for whom they are easy and ask about keeping practices, really.
Have 4 kinds of them myself, the worst part is that they close for a months, without opening polyps for a feeding. It shouldn't be dormancy - seems, it's only for cold water species.
What you may try:
place it in the dark place, in good flow for removing settling detritus from the skin, upside down or not - some of mine disagree to be upside down. They most likely open in the dark, or it their habitual time (some of mine do that at 3 pm in unlit tank, some - night and the earliest morning. Invariably closing after light is on, even 18W PC at 6-7").
If and when are open - feed, repeatedly, for prolonged periods.
Food - zooplankton and good quality artificial substitutes (Fauna Marin, Reef Roids - Rotifeast (or something like that), Golden Pearls, Oyster eggs, rotifers, cyclops, decapsulated brine shrimp eggs, ZoPlan, finest particles after blending seafood).
Depending on size of the mouthes of your particular chili (you may try macro mode digital camera, or Optivisor, or +4 reading glasses from dollar store, to see what size of food you will need). I would vote for mix of different particles, 150-600 micron. Cyclop eeze is up to 800 micron, only for big-polyped kind.
Here you can see devoured Cyclop-eeze:
here - ZoPlan and smallest mysis particles, less visible:
Cyclop-eeze will be way too big for this miniature kind:
Let polyps get several pieces of food, few to several times a day.
If your get dormant - move it in dark windy(flow) place in the tank, and don't give up. It may open 4-5 months later, skinnier, but alive. Watch for irritation by bristle worms.
Good luck!
And if you find or notice yourself anything about their better keeping - post for all of us, OK?