HI, I was having the same problem, I had to manually enter the hidden network details in order to connect, which was very annonying.
I tried resetting the network settings and then restoring the device (happened on an IPad and IPhone), which only lead to more frustration since it didn't solved the issue.
Anyway, since that happened on my personal wifi (yes, I might be a Little paranoid by hiding the network) I decided to take a closer look into the configuration settings and enable wifi broadcast if necessary, however I noticed something regarding wifi security settings: on my router they were setup as WPA-PSK/WPA2-PSK AES, however when I connected to it using my iPhone/IPad I selected WEP since I didn't know any better at the time, since it connected I was assuming that was the right setting. After looking into the wifi security options, I then reconnected to the hidden network but using WPA2 option, it got connected and so far it has reconnected automatically (I am testing putting the devices in airplane mode, when usin WEP options it didn't connect to hidden wifi, however now it connects every time so far). I didn't have to enable wifi broadcast after all.
I can see a couple of things wrong with IOS code:
1) Why does using WEP Works for public wifi but doesn't on hidden wifi networks? It should behave the same for both otherwise it is confusing.
2) Why does it allows to connect using the wrong security setting? This also adds to confusión on users that are not experts on networking issues.
Anyway, if that is in fact a bug ion IOS 10.x I hope Apple coders can debug it and fix it.
Hope this helps to anyone still having the same issue as mine, good luck!