That's a butterwort.

What type of soil is it in? It looks like it's too wet. 50/50 sphagnum peet moss, perolite ( spelling?) with a good helping of gardening sand, might help. I'm just adding my two cents, no expert at all. But my plants seem to be doing better with the sand added. Helps with the drainage.
I'd start with new soil first, clean it up, sit it on top of the soil, push the soil up to the roots.when you water it the soil will fill in around the plant without hurting the tiny roots. And don't drown it.
Let me know how it goes! Good luck!

If it is a Sundew, avoid soil (you probably already know that if you are using distilled water. I use peat/sand/perlite in a 1:1:1 ratio. And my Sundews stand in water. They are bog plants.

It does look like a butterwort, which go dormant by growing shorter leaves and less sticky ones. I grow mine in two parts perlite one part peat and it does fine, same advice if it were a sundew tho. Good luck!

Where did you get it and yeah I'm pretty sure it's a butterwort. Determining the seasonal nature of its habitat is crucial to its survival.