Time Machine could not be accessed, network password problem

I'm running OS X El Capitan (10.11.6) and after running the latest set of updates from the App Store (Security Update 2016-003, Safari 10.0.2, XCode Command Line Tools 8.2, iTunes 12.5.4), Time Machine has stopped being able to access my shared ReadyNAS TM share. I'm running latest firmware (6.6.0). The error reported from the Time Machine prefpane is:

Time Machine couldn't complete the backup to "nas".
The network backup disk could not be accessed because there was a problem with the network username or password. You may need to re-select the backup disk and enter the correct username and password

In the console, I see:

com.apple.backupd[2950]: NAConnectToServerSync failed with error: 80 (Authentication error) for url: afp://ReadyNAS@nas._afpovertcp._tcp.local./timemachine
com.apple.backupd[2950]: Authentication error (80) - the correct user or password info may not exist in the System.keychain or the server may no longer allow access for this user.
com.apple.backupd[2950]: Attempting to mount network destination using alternate URL: afp://ReadyNAS@nas.local/timemachine

It doesn't help if I delete the relevant keychain entry, remove the disk from the prefpane and re-enter the credentials when prompted. Rebooting the Mac makes no difference. The shared Time Machine settings in FrontView admin look fine. It successfully backed up an hour ago. I fear something in AFP has been broken by the latest update...