Probably too much moisture. Nothing you can do about the rain, but definitely don't water any more until the soil dries out. Vinca loves hot, drier conditions (though also does great in soil with average moisture content).

Also, you said you planted about a month ago - up here, the soil was too cold a month ago, so yes they may have rotted out due to cold, damp conditions. Warm season annuals are best planted when the soil temps are warmer (which didn't happen where I am until the end of May, and just barely then).