100% agree. You'd start to think "Anna doesn't like us" and just move on. Despite what they're going through, some level of responsibility falls on them to express a sense of "it's not you it's me", if they legitimately do want to remain part of the friend group. Not engaging with the friend group is effectively the same as not being a part of it. If the "pleasant feeling of being included in the group" is the entirety of your involvement, it's actually a somewhat selfish and shallow position after a while. That's not to say that the group has to ban her, but at a certain point there is no valid reason to engage with someone (in a group context) who doesn't engage back.

If you have friends you think are depressed or have something else going on, by all means reach out, but thats not the same thing.