Since going paleo a year and a half ago, I can count the number of colds I've had on one hand (before paleo this happened several times per year). Every single one occurred following a weekend of both traveling and breaking my otherwise strict diet.

In each case, I lost my appetite and inadvertently fasted for two days, and felt noticeable continuous improvement in my symptoms over the period, until my cold was essentially gone. My belief is that this is caused by the fasting (and studies do show increased immune function during fasting), but I don't get sick often enough any more to do a rigorous test of the theory!