I'll walk you through it. (I just hope that the UI labels wiil fit exactly; as I use the Dutch language version, I have to guess a bit for the English version)
Go to Settings and select the details of your home wifi network, using the blue chevron icon on the right.
You'll see a bar with DHCP selected, and most of the items like IP address filled. Take a pen and write them down.
Now click on Static. The underlying fields will empty. Fill them in with the values you just took notes of.
It might make sense to fill the DNS field with multiple server addresses, separated by commas. That way if one DNS server goes down, your system will be able to switch to another. I took a list of fall-back servers from my service provider.
Leave the page by clicking on the Wi-Fi Networks arrow in the left hand top corner.
That's it. Just for this network, you've now switched to using a static IP address. All other networks will still be using their own dynamic settings.
One more thing: if things don't work right away now, you might need to choose another IP address.
Just pick one that is a notch higher than the number of systems you use. E.g., my IP range starts at 192.168.0.1 (my WAP/router). The local DHCP server integrated in my router gave 192.168.0.2 to my iPad, .3 to my PC, .4 to my wife's Mac and .5 to my iPhone. If these addresses for some reason would not work using static IP addresses om my iOS devices, I would use .10 and .11 respectively. You might try something along these lines.
A guess as to what all of this means.
I noticed, just once, that my PC gave of an error message saying there was a conflicting IP address on the network. This got me to think the following.
Perhaps when the router sends network trafic to the iOS devices, every now and then for some reason they do not respond correctly. A dialogue ensues to issues a IP address to the iOS device. However, the device itself still assumes it has the previous address. Conflict.
When I switch the device to flight mode and back again the situation is resolved by flushing caches and then re-requesting an IP address. At some point in time, the whole thing will cycle again and again.
This erratic situation is bypassed by claiming a permanent IP address for the iOS device. Is simply will not request any new address, and any faulty response to network traffic simply results in a retry and some microseconds of delay. On the other hand, you yourself will now be responsible for handing out addresses that do not conflict with others.
For that last task, you might consider using some kind of LAN scanner. I use Advanced LAN Scanner 1.0 beta on my PC and Scany on my iOS devices. They'll give you a clear picture of what addresses are in use at a given moment.
If my guess as to the origin of all our troubles is faulty: just neglect it. It is neither here nor there anyway.
I hope my little instruction will be of some help to you: let me know!