Well, the issue with ours appears to be related to the BLF notify messages 3cx is sending the devices. I found out how to fix it / workaround almost the same time Fanvil support suggested using the latest firmware and disabling an option. 3CX support, through the vendor that sold us the system, has yet to identify the issue or suggest a fix. If they "approve" the latest Fanvil firmware and update their template to disable the option that needs to be disabled, that appears to be the fix.
Fanvil x6 BLF Status issues (not updating and getting “locked” on wrong status) ie BLF keys just flash red all the time or remain solid red, even when they should be green.
Fix or workaround is found on firmware 1.6.2.1 (3cx not official yet) or 1.6.3 (Fanvil official) and unchecking under Line->Advanced Settings -> “BLF Dialog Strict Match” or “Enable Multi-Dialog” This caused all the BLF keys to revert to their proper status and not get “locked” on a wrong status at random in the future. This is as of 3cx 15.5 SP5
Firmware 1.4.4.2 doesn’t have this option and is the most recent "official" firmware approved by 3cx.
The code in the config is <BLFDialogMatch>0</BLFDialogMatch> (0 is off , 1 is on) even when the front end on 1.6.2.1 calls it Enable Multi-Dialog.
This could be related to your issue but seems like it's a Fanvil+3cx issue.