The point of the tooling is that you describe what you want your deploy to look like, and it updates the deploy to match the description. If you delete something from the description and it stays running, that would be very confusing.
I haven’t used their particular tool (ArgoCD) but the ones I have used include an option to keep specific pieces of infrastructure around even when it’s deleted from the description. That’s absolutely what you should be doing for anything that stores data.
It's not too bad. There are two approaches to this one in AWS: 1. You can mark specific resources like db and volumes to be retained on stack deletion. 2. You can't delete some resources easily without deleting the content. Wanna delete a bucket? Explicitly delete all the objects first.