Please test after taking each of the following steps that you haven't already tried. Back up all data before making any changes.
1. If Handoff has never worked, verify that the Mac is capable of using it. Hold down the option key and select System Information... from the Apple menu. In the System Information window, select Bluetooth from the list on the left. Near the top of the summary of "Hardware, Features, and Settings," you should see this line:
Handoff Supported: Yes
In rare cases, you might not see that indication, even though you have one of the models that is supposed to support Handoff. That could happen because of a hardware fault or a corrupt OS X installation.
2. Follow the instructions in this support article. All the devices using Handoff must be connected to the same Wi-Fi network. If the Mac also has an Ethernet connection, disconnect the Ethernet cable.
3. If Handoff still doesn't work, on the mobile device, turn Handoff off and back on as directed in the support article. On both devices, turn Bluetooth off and back on. You might have to restart a mobile device to get it working.
4. Reset the NVRAM.
5. No Continuity feature will work if either of the devices is connected to a VPN.
6. Triple-click the line below on this page to select it, then copy the text to the Clipboard by pressing the key combination command-C:
/var/db/CoreDuet
In the Finder, select
Go ▹ Go to Folder...
from the menu bar and paste into the box that opens by pressing command-V. You may not see what you pasted because a line break is included. Press return.
A folder named "CoreDuet" may open, containing one or more files with names beginning in "coreduetd." Move those files to the Trash. You may be prompted for your administrator login password. Restart the computer.