A client recently experienced an issue where a key query-based group was disassociated from its query.  Once this link is broken, there is currently no way to re-associated a group with a query. You can use the query to "Add" members to a group, but won't rebuild the full group membership.  Even if you just wanted to "add to" the group using the query, you cannot schedule it to happen automatically.  

The impact of this is that we had to delete the group and use the query to create a new group that is associated with the query.  The problem is that we then had to edit all of their other queries and campaigns that used this core group as criteria.  Just deleting the old group and recreating the new group with the same name won't automatically replace the group in the other queries because the underlying group ID changed.

From what we can tell, there are two possible scenarios for how this "un-linking" can happy.  Either the query is deleted, leaving the group a static group, or the query is used to "create a new group" instead of rebuilding the existing group.  Once you use the query to create a new group, it breaks its link to the original group.

What we would like to see considered is a way to link groups to queries "after the fact."  That way if something like this happens again, we won't have to delete the group and create a new one (and do a bunch of other manual edits) to resolve the issue.