Yes and no. iOS 7.1 blocks cables that are not Apple certified. The primary reason is that the cable is complex; it has 3 microcircuits in the phone end of the cable that perform isolation, pin swapping (so you can plug it in either way) and digital to analog conversion. Those are proprietary chips only available from Apple, so any cable that is not certified probably will not be compatible with the phone and can possible damage the phone (there are actual cases on record). The other reason is that Apple has a patent on the Lightning technology, and they are protecting their patent.
Griffin I'm pretty sure is certified; they are a close Apple hardware partner. And as it has worked in the past on 7.1.2 Apple's check for counterfeit cables is not what is causing your problem. Most likely either there is dirt in the Lightning connector on the phone, or the cable has failed. Try cleaning the connector with a wood or plastic toothpick, and inspect it carefully.