Erratic cellular data settings

If you feel lonely and ignored when nobody seems to have a solution when your software acts erratically.  Take heart!  It happens to novices and gurus alike.  You are not a "dummy".  It just takes a lot of time to get all the necessary information to pinpoint the problem. 

I sent the following to Consumer Cellular after an abrupt disappearance of a long-standing annoying problem.

To avoid using up cellular data I turn cellular data on and off on my iPhone 5s.  With iOS 9 it became a nuisance because the settings would not change quickly, often it could take two minutes.  This doesn’t happen on my wife’s iPhone 5c with iOS 8.

I thought the problem could be iOS 9.1.  The problem did go away when I installed iOS 9.2.  Then the problem came back.

Yesterday, we changed our data and voice plans, splitting our account into two accounts.

Today, I can turn cellular data on and off quickly.  No change in iOS.  No change in other settings.

Could it be something Consumer Cellular or AT&T is doing?

This also makes me wonder it I changed my bank prematurely.  Would
Consumer Cellular now let Republic Banks software operate smoothly?  Nope, it still gives system error after I enter my password.

Anybody in CC have the time to really look into this?  Have any other users reported a similar problem.

Note added 2016-01-18:
For one solution, see http://magree.blogspot.com/2016/01/more-on-erratic-iphone-cellular-setting.html.