I have had many click booms (delayed ignitions) and failures to fire with CCI mag primers. In the failures to fire the primers actually went off, the powder inside was clumped and part burned but the round did not fire. This happens primarily in loads over 75 grains and the colder it gets the more pronounced the effect. It is caused by the CCI primers not having enough Brissiance to ignite large powder loads. If your powder is clumped, or you are getting click booms, switch to Federal 215s. They were specifically designed for Roy Weatherby to set off the 378 Weatherby and 460 loads reliably. They are MUCH hotter than CCIs. Next hottest is Winchester Mag.
If the primer failed to go off at all, you already have lots of good advice on things to check, but the number one cause its primers not set deep enough and or primer pocket uniformed to be too deep. After that it is firing pin issues.