Even with continuous brewing, don't you have a distinct mother/baby separation? When you have a thick-enough baby (maybe 1/4"), I'd pull out both of them and just leave the baby in there. Put the mother in a "hotel" - a separate jar where you also add a cup or so of starter each time you pull out a mother. Do that every week to 10 days so that you're always using a nice fresh baby.
With the hotel as backup, if you ever do get contamination you have a separate supply of mothers waiting & you also have some to give away to friends.
I don't use the continuous brewing method myself so apologies if it doesn't work the way I describe.