Depending on where I am in my training, I run between four and six days a week. So that means between 1 and 3 rest days.
How do you pace your runs? even when running six times a week, I wouldn't do more than "three" quality sessions with the remaining sessions run at an easy recovery pace.
For your three consecutive days, if you run the first day at a high pace you probably want to run the second and maybe the third day at a lower intensity.
Personally, taking a week off now and again is always worth it and doesn't have any major impact on your fitness.