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Not if the cell connection is actually turned off I would think, as seems to be the case for the OP.

Engineers were given the task of designing a "phone". They designed it to maximize the battery life. Obviously if you can shut off one of the radios to increase battery life it would be the wifi radio. OP is trying to use a phone in a manner for which it was not designed. Can it be done? Sure, but there are something's he will have to learn to live with.

That being said, the one experiment I have not tried and I think might work for OP is to turn on "airplane" mode. That turns off both radios. Then leaving airplane mode on, turn on wifi. That may over ride the system but like I said I haven't taken the time to check that.
 
Engineers were given the task of designing a "phone". They designed it to maximize the battery life. Obviously if you can shut off one of the radios to increase battery life it would be the wifi radio. OP is trying to use a phone in a manner for which it was not designed. Can it be done? Sure, but there are something's he will have to learn to live with.

That being said, the one experiment I have not tried and I think might work for OP is to turn on "airplane" mode. That turns off both radios. Then leaving airplane mode on, turn on wifi. That may over ride the system but like I said I haven't taken the time to check that.
I could be wrong, based on the way the OP is presented I assumed that's likely what is already being done there (Airplane mode and WiFi on) so if that's the case it's odd that it would still disconnect in that type of scenario. If that's not the case, then that certainly would be the way to try going about it.
 
I don't think that the default iOS coding is to switch off wi-fi in the sleep mode.

My opinion is based upon that my home wi-fi it will stay connected constantly even in sleep. When I wake the phone it does not flicker from 3G to wi-fi. It is just always on wi-fi.

However when at work and in pretty much every free public wi-fi spot I have used it pauses the wi-fi on sleep. Every time I unlock the phone I see if flick from 3G to wi-fi.

When I am at friends and using their own private router I get the exact same results as home where it is connected constantly.

I'm wondering is this not a battery saving feature but a security feature as public/free wi-fi is usually an open connection with no password?
 
In my almost three years of iPhone experience, from 3GS to now 5, I have always noticed that the phone goes to 3G/LTE when sleeping, and when I wake the phone, it reconnects to wi-fi in 5-10 seconds.
 
When I first got my iPhone 5s it would always stay connected to my home's wifi until recently I started relizing that it would automatically disconnect from wifi whenever I lock my iPhone
 
When I first got my iPhone 5s it would always stay connected to my home's wifi until recently I started relizing that it would automatically disconnect from wifi whenever I lock my iPhone

Yeah, that pretty much has been typical behavior for iPhones for a long time now.
 
With cellular data disabled my 5s will stay connected to Wifi. With it locked and showing a black screen, it will wake, show a notification for new email, show the slide to unlock message, and go back to black screen if ignored.
 
So I currently dropped my cell service and am using my iPhone 5S with nothing but wifi and I've starting noticing that my phone drops wifi when the phone is locked. This can't be normal right? I was under the impression iOS devices remain connected to wifi even when the phone is locked, so you can get updates or notifications in the background. Has anyone else experienced this? It's annoying because my phone will be locked and I won't get any messages until I turn on and unlock the phone.
Right now, I solved the disconnect problem for myself.
It happened the same like you explained on my phone. After I changed my router name to Jäger-Wlan the problem went in. Also in the manuell connecting to the WIFI was weird because my IPhone 5s showed me the router name as J?ger-Wlan. A half year later (today) i had the time to investigate the problem and found out that my WIFI wasn't saved in my phone and Web-Whatsapp was only working, if my phone is unlocked and connected. Today i changed my routers name to Jaeger-Wlan and the disconnects are gone. I might think IOS devices have issues with ä,ö,ü and maybe more signs which are not compatible with that devices in networks. Maybe your router name is the problem. Check it and try a simple name like Home-Wlan or something like that. After the change you have to reconnect all your devices with the network password again.
 
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