Periwinkle can be subject to canker and dieback which will cause it to wilt and die back to the ground. Take a sample (dig up some) of it to your local cooperative extension office to see if this is what's happening.

Otherwise, look to cultural conditions. Too hot, too dry, too much sun can be a deadly combination. Too dry in winter combined with a windy site can cause desiccation and leaf dieback, too. Too much fertilizer or salt from a nearby road, driveway, or sidewalk, all these things can cause problems.