Rest week

Not at all. In fact, sometimes it's a bigger benefit that you might realize. If you're feeling tired/lethargic and don't take a rest, your body's stress/immune system shorts out and you can get sick, which possibly will lay you up longer than one week. You don't have to completely stop everything, just take some leisurely evening walks that week, enjoy a short bike ride with the kids, or whatever. Go dancing!

You won't lose your base in one week, but trying to train fatigued won't increase it at all, and could actually decrease it.