Just this morning my iPad4 wouldn't connect. Looked at the settings and it had a bogus IP address and DNS setting. Hit the Renew Lease button and it picked up the correct one and its working fine. But it shouldn't be screwing up the IP lease in the first place. None of my other wireless devices ever have a problem, only my iPad.
As I said, people have been complaining about this issue on the Apple support forum for two years and Apple still has not acknowledged a problem.
Could be because there's an Apple problem, could be because they followed the DHCP spec and routers aren't. Impossible to tell without a packet trace.
Internet is full of folks whining about interop problems between vendors of all sorts from software to networking to hardware. Rarely does anyone take the extra mile to analyze the problem when new devices are less than a tank of gas in a pickup truck, ya know?
Not worth any spare brain cells unless its your problem and you know how to catch it in the act at the low level protocol stuff.
First thought: Was the IP one of the 169.x.x.x "auto-assign myself an address" range? That BS idea to "help" people build ad-hoc networks has been a horrible idea from the start. An attempt to remove all brain cells and often causes more problems than it's worth.
Second thought: Any rogue software or devices acting as DHCP servers on your LAN so you have two at the same time?
Third thought: Set DHCP lease time to something very high (a week or more) to slow down the symptom.
Fourth thought, and my favorite: Get the MAC addresses from your devices and nail down everything to its own IP. Can do this with static IP also, but I tend to do it at the DHCP server. Then keep a spreadsheet of what gadget is what IP. Saves headaches troubleshooting later, makes networked printers and scanners happier (no relying on broadcasts to find them by name, network is much less chatty and clogged with garbage), etc.
Does Crapcast let you access the router's DHCP settings? Logs? Wifi connect/disconnect logs? I bet what you'll find is the iPad is aggressively "roaming" and trying to go back and forth between wifi and cellular data all the time, confusing the hell out of itself and the DHCP server. With its IP locked down to a single IP for that Wifi network, it'd behave much better when it does that.
I've seen all three of our iPads (confirmed with Wireshark sniffing) say they're on Wifi or cellular when they're actually in the process of switching networks and are truly talking on the other one. Also seen it with Karen's Samsung tablet. Locked down all the IP addresses using MAC address assignments in the router, no more problems. They still do it, but when they rejoined the wifi they worked consistently.
Fixed the wifi disconnects using Apple Airport Expresses in Network Extender mode. I'll take the speed hit for the multiple hops on wifi to not be dropping off anywhere on the property. AirPort Extreme at one end of the house, and two Expresses extending both 2.4 and 5.8 networks strategically placed in the structure to cover indoors and out, including the garage. Eventually I'll cable Gigabit Ethernet to those locations so the extension isn't done wirelessly and it's more a multiple-AP roaming network configuration.
(Plus its also fun to look at the logs and see if the various devices are connected to the "closest" AP or the one at the other end of the house as you walk around... Some devices favor 5.8, some 2.4, all favor "n" over "g" or "a" generally. The work laptop Intel chipset with updated drivers actually lets you set this "affinity" stuff.)