(More as information for everyone and not just yourself.)
QNAP make NAS devices, that is a box with its own internal storage, processor, network interface and software. Like almost all NAS devices the QNAP box is running a variety of Linux.
Again like almost all NAS devices - especially those using Linux it runs a version of the open source Netatalk software to implement support for AFP. Where the QNAP might fall down a bit is that I believe they are not as quick at updating their version of Netatalk software as for example NetGear.
As others have mentioned in the past Apple has made subtle changes to the AFP protocol and this means the Netatalk project developers have had to discover these changes and make matching changes. Whilst I cannot guarantee it, I suspect that Apple have stopped making changes to AFP since they have dropped some not so subtle hints that they intend to discontinue AFP at some point.
Apple now want everyone to use SMB instead and have been saying so for the last few years. Initially this resulted in a potential problem since they had originally left Time Machine still only able to work over AFP and not SMB. With the aforementioned not so subtle hints that AFP was doomed this left a gapping hole. I did therefore each year a new version of OS X came out remind them of this via the beta-test program. When Sierra came out Apple finally resolved this issue. Sierra can now backup over SMB to a suitable SMB server.
A suitable SMB server does not have to be a genuine Mac server. This time Apple have actually provided official technical information allowing other software developers to make sure their SMB implementation is able to do the things Time Machine needs. See https://developer.apple.com/library/content/releasenotes/NetworkingInternetWeb/T ime_Machine_SMB_Spec/
Going back to NAS devices, just like Netatalk is the software typically used for AFP, SAMBA is the software typically used for implementing SMB in NAS devices. Whilst the current official release of SAMBA does not yet have all the changes needed for full Time Machine compatibility added - something I am surprised about, the SAMBA developers are aware of this and do appear to be working on this and a pre-release version may have already added all the needed changes. See https://bugzilla.samba.org/show_bug.cgi?id=12380
I would suggest checking for any available software updates for your QNAP and installing them, this may include Netatalk updates. At some future time a further QNAP update will hopefully also include a SAMBA update with the required changes for that as well.
For what it's worth I currently use a NetGear ReadyNAS as a Time Machine server via AFP and find it no less reliable than a genuine Apple Time Machine solution. If you want the latest, most compatible, genuine 100% Time Machine solution then using a Mac running Sierra and Server.app as a Time Machine server is the best option.
A Time Capsule would not be anywhere near the best option, not only does it only do AFP for Time Machine backups, it has already been officially discontinued and is therefore unlikely to every get Time Machine over SMB support added to it. This also ignores the fact that the hard drive inside a Time Capsule is notorious for failing.
