That is rather unusual! How long has this been going on? Do you both have the same type of iPhone? Is your ios completely up to date? Are either of you on wifi when you have tried to do this?
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This is the best debug steps I have seen (from igeeksblog.com)
Make sure you also reboot your phone as part of the debug process. (Press and hold home button and sleep/wake button together for 10 seconds then let go). -- Don't miss that important step!
How to Fix AirDrop Not Working In iOS 8
You can tap on Everyone or Contacts Only depending on your wish and the need to do so.
Reboot your device. Sometimes your device may stop functioning properly due to some technical glitches. The best way you can solve this temporary glitch is just by powering down your device and then starting it off again.
Hopefully, your AirDrop bug will be fixed now.
AirDrop makes communication between like devices so easy. Initially, it was started with only Mac to Mac. Then it became iPhone to iPhone thing. And now with iOS 8 and OS X Yosemite, it is allowed across all Apple devices. The so called cross – communication has been upgraded to a new level in order to bring more efficiency for Apple device users.