I'm a C25k graduate and am training for my first half marathon (I just finished my first 10 mile run yesterday...non-stop I might add)
If you research running sights, you'll find that most people advise against running every single day (at any distance). I am told your body needs time to recuperate and your muscles need time to restore.
Having said that, there were days when I needed to adjust the C25k program to fit my schedule and actually ran 2 days in a row (instead of the suggested rest break). When I did, I definitely
felt it and my second run wasn't as successful physically or mentally. My mind would become "tired" more easily when I ran back on back days especially when the time periods began to stretch out longer. I found that when I rested, my body felt stronger and mentally I was ready.
It all depends on your current level of fitness but I wouldn't advise doing back-to-back days once you get to the longer runs.
I graduated from C25k around May/early June of last year. I've run approximately 4-6 miles a couple of times per week since then. Now, I'm doing longer runs (I did an 8 mile, 3.3 mile speed run and a 10 mile long run last week). I still benefit from resting although I usually cross train on those off days.