Hi Steven, VFTs won't starve to death, that's for sure
The trap don't close basically due to a few reasons:
1. The trap had been triggered for several times. Itchy hands will exhaust the trap.
2. The trap already too old to work normally.
3. During dormancy.
4. You have to touch the same hair for at least twice OR touch two different hairs at once (almost at the same time) to trigger the trap.
Give your VFTs plenty of sunlight, at least 8 hours if you can, they love sunlight. Like what David said, a photo of the plant will help to rectify the matter.