I am writing specifically to address the question you ask in your post: "What's the policy that someone is enforcing here to delete comments?"
In your post, you didn't mention what exactly your comment was that got deleted recently. Mod Chocolate points out that your comment was "Thank you for your feedback." Thank-you comments are discouraged. Once left, they should and more often than not will be removed. And this is a network-wide policy that's been part and parcel of the StackExchange model.
Well, years ago I asked a similar question on a different meta site in the StackExchange network, and I received a really good answer from an ex-mod on that site who also happened to be a moderator on Japanese SE, @snailboat (snailplane/car). As time went on, I discovered other sites in the network, whose meta sites are no stranger to this kind of question. Combining what I have seen across the SE network and learned over the years, I think the simple answer can be found here, emphasis mine.
Comments are temporary "Post-It" notes left on a question or answer.
Pay attention to this part
When shouldn't I comment?
Compliments which do not add new information
I don't think it could be said more clearly than here in the site Help Center:
Please do not add a comment on your question or on an answer to say "Thank you". Comments are meant for requesting clarification, leaving constructive criticism, or adding relevant but minor additional information – not for socializing. If you want to say "thank you," vote on or accept that person's answer, or simply pay it forward by providing a great answer to someone else's question.
You said "I don't so much mind "thank you's" being deleted as long as the person they're directed toward has had a reasonable chance to seem them." Well, the StackExchange model was designed and community-improved to obviate the necessity of having to post such comments.
Some users flag them, and the system may even automatically remove thanks comments upon flagging, which is apparently what happened here with your comments, as Chocolate suggests.
Should a "thank you" comment be flagged?
A "thanks" comment that doesn't provide any specific praise about the answer is usually not constructive, and almost always qualifies as "too chatty" as well... When such a comment is flagged, it should be removed unless it contributes something.
This has been repeatedly brought home by a number of Meta SE posts. In her answer, ex-mod and longtime StackExchange contributor snailboat clearly states:
Although there's been some disagreement in the past, I think the general consensus looks something like this:
- We don't need thank-you comments on our site.
- If you flag them, they should probably be removed.
- They're only a minor problem, so the flags aren't a high priority.
I am not saying the nice gesture is not appreciated. It is. But the site has other options specifically designed to do what a thank-you comment does and better at that. If you appreciate an answer, upvote it (and/or accept it if you are the questioner); if a comment has helped you, throw a like on it to show your gratitude. Simple as that. You mentioned that you wanted to show "gratitude whenever possible" but as is with every bit of contribution on StackExchange, across the entire network, the contribution isn't about any one of us. It's from the community, by the community, and for the community. So is your gratitude. Upvoting answers/questions and liking comments are great ways to show appreciation while keeping answer grading and appreciation anonymous, democratic, and community-based.
So unless you have a compelling case against showing your appreciation anonymously, upvoting and liking are the way to go.