desert i don't think means deserving. It comes from the latin desertus which means to "make barren or empty/forsake". I think in this context it means to have something fail or be abandoned at a critical moment.
The person you’re replying to is correct - “desert” is in some contexts an old word that’s pronounced like “dessert” but spelled with one “s” that means “the punishment that one deserves”.
https://www.merriam-webster.com/words-at-play/just-deserts-o...