Here is an update: it appears that the WPA encryption key was the problem. I had been using an encryption key with 63 random printable ASCII characters generated by Steve Gibson's website (http://www.grc.com/passwords.htm), that looked like this:
&bdM^4_:?9ZE|rYE^K.%]Fm]i$DG0?B&_T4u&!Th"yTf&k-t|{Iyy6]Ir0[t}[/
(Not the actual key.)
When I switched the encryption key to 63 random alphanumeric characters (from the same site), that looks like the following, the problem went away.
0Rqfg4UGubTt9688yyj2Ih5rxJhrz7xvWRlO8989yTZDM3fDrBgnWrysTS8MUkB
(Not the actual key.)
I have not done any testing to see if this is a general rule, but at least in my case, it appears that the characters in the WPA encryption key prevented the router from reloading the stored configuration.