Does GOG have a way that they announce what games are being removed or retired from the site?

deleted

If what you mean is whether they announce the removal of a game in advance, as of late they're doing it here in the forums, but rarely (if ever) in the main store page.

On the other hand, if what you want is a historical account of all the games removed (and sometimes re-added) to the GOG store:
https://www.gog.com/forum/general/games_removed_from_the_gog_catalogue_by_year
https://www.gogwiki.com/wiki/List_of_games_removed_from_GOG

There's this thread as well but it appears to not be up to date:

https://www.gog.com/forum/general/list_of_games_removed_from_gogcom

Linking to it with the hope someone can review it since it's like the first hit on a google search.

That topic's OP links to the very same GOGWiki list linked to by muntdefems; and that IS up to date (though it has a few little inconsistencies/oversights). I also link to the same page multiple times in my breakdown that muntdefems also linked to.
Frankly, as long as that wiki exists, and somebody with access is willing to keep that page updated, I see little reason why anyone should need to simply re-post the exact same info in this forum. (My list is somewhat distinct from the wiki list in that it's more about statistics than names and exact dates).

Things were a little fuzzy last night. Still are today.

I pointed out the thread since it;s the first return for me via a google search. I made the suggestion since I'm sure many folks would no go any further in their search for such a list.

Maybe posting links at the bottom of that thread to where folks can find such a list would be a good idea.

I've once brought up a request for a notification email system, that GOG users could sign up for if they wish. I would love it if they could implement something like that.

Thanks everyone. This may not be a good example because I know there may have been some legal issues here, but it appears the Star Control series was removed and I was pointing it out for someone to buy. But it appears that they can't now. So I was curious. If there is any kind of schedule, I want to make sure that I pick up any on my wish list that may be going away. Thanks everyone.

There is no schedule, as there are multiple factors that can result in a game's removal. It can be something that the GOG team is aware of one month in advance (like the Bohemia catalog) or a takedown notice that results in a game's immediate removal, with no time to warn customers beforehands (Call of Cthulhu: Dark Corners of the Earth).

I've been meaning to ask: If a game is removed from GOG does it still stay in your collection here for later download if you have already bought it?

Yes.

That's great! Thanks for the reply! :)