Upgraded this box to iOS 10.3 to see if that would help. Same problem even after upgrade and of course a cold boot, so even a reboot did not clear it.
But now I have fixed it. I managed to work around the bug. I did a 'forget network' and then the problem was cured, for how long I don't know. I suggested to Apple that I think it would be a good idea to report this as a bug. It is definitely state-dependent, and we know it can be cured by deleting a data structure.
It could be some corruption of the database of wireless Lan settings, or else some related data structure. The machine can not possibly be running low on RAM as no other processes were running on one occasion. Unfortunately I have no idea how to get it into this state, but once it is broken it remains so forever so it seems. It failed in this way dozens of times over several days. Also since I had just cold-booted the o/s, it is not due to corruption long-term, and it has to be something messed up that can survive in _persistent_ storage and continue to cause trouble even after a reboot.
It is going to be a nightmare for Apple to reproduce. The question for developers is, what could cause the machine to reject settings or throw an error so they are not retained when you enter them in the static ip page. The exact values entered seem to be irrelevant, I tried various different values on two different machines. An example that is known to fail (amongst many others) is IPv4 = 192.168.1.22 netmask = 255.255.0.0 and no other values entered. It still fails if other values are given as well e.g. Default gateway and dns server. It fails if different netmasks are used and also fails with 10.0.0.0 netmask 0.0.0.0 for example.
There are three entries showing in the list of wireless lans, only one of them has a saved password and other settings associated with it. I did not try repeating the test with a different wireless Lan, and in any case it wouldn't have been an ideal test as it would have meant entering a password and presumably creating data structures from scratch anyway.