Had the exact same issue today with our 2 iPhone 5 and 5S after upgrading to 7.1 (update wirelessly). Could not figure out why AirDrop stopped working after the upgrade. Then decided to connect iPhones physically to the computer with iTunes running. A screen popped up asking if the computer is a trust computer. Once hit 'Trust' on the phone, disconnect it from computer, and restart the phone, AirDrop came back with blue color and 2 phones could talk to each other again!
I think this 'trust' verification is new in iOS 7.1, which probably broke some security setting in AirDrop. Give it a try to see if that works for you. Good luck!