@Anna N -- near as I can tell the rye levain is invincible. I've stopped feeding it mid-week, I just refrigerate until Thursday evening, take it out, then feed the amount I need Friday night and refrigerate the remainder until the next week. The wheat is a bit more finicky, I feed it mid-week as well, but it's still pretty robust.
ETA: As I reread I realize that post was not exactly clear. Here's what I do:
Friday night: feed the levain in two parts, one for maintenance and one for what I'm using to bake the next day. Refrigerate the mainenance portion.
The following Thursday (six days later): take the maintenance portion out of the refrigerator, but don't feed it, just bring it to room temp.
The next day, Friday: Repeat the previous Friday...