I coach a runner who really enjoys snowboarding. This athlete will travel to Mammoth Mountain on a monthly basis, trying to catch great powder. This athlete has modest goals for running, and certainly is only motivated by the desire to improve, not a specific race.
One of the issues which we discussed is that during these typical 3-day trips, it is important that they run at least one time during the 3 days. The athlete claims the weekend spent snowboarding is taxing on the legs and not really a rest day, which I understand and agree with. But in the sense of training and specificity, you need to keep running consistently to improve.
To better define consistency, I would say you should not have a 3-day break from running. You can get away with 2 days once a month, maybe twice, but once you go beyond that, you are beginning to lose opportunities to improve, and affect your consistency. If you have very high, competitive goals, I would reduce that number to not missing 2 days in a row of running.
If you're injured, that's a different story. But even then, if you can keep your injury healing time down to 2 days, maybe 3, you're not losing much fitness if you've been consistent. Once you go beyond that, bad news. So when you see an injury coming, give it the attention and therapy it needs right away, and you can better keep your consistency, and not lose fitness.
Remember, you lose fitness about 3 times faster than you gain it. 2 days off can help you recover and stay healthy, but once you get to 3 days off, you're losing fitness.