Just wanted to add that I'm having the same issue reported above with an iPad Mini 2. I'm also using a BT Home Hub 5 with separate SSIDs for 2.4GHz and 5GHz. The iPad connects to 5GHz, but will typically stop working after < 30 seconds. When I connect to the 2.4GHz network, I have no issues.
My iPhone 5S and MacBook Pro are both able to connect to the 5GHz network without issues.
I actually first started encountering this issue back in late August, long before upgrading to iOS 8. So, I'm not convinced that this is an iOS 8 problem. Originally, I had assumed that it was a hardware fault. I was planning to take it into the Apple Store, but I first decided to test the 2.4GHz and 5GHz networks separately to see if the issue only occurred on one frequency so that I would be able to replicate the problem in store. Turns out that the issue was indeed confined to the 5GHz network, so I decided to wait for iOS 8 to see if that would fix the problem.
Like others, my solution is to keep the iPad on the 2.4GHz network. However, this can be a bit tricky because the iPad is able to obtain the password for the 5GHz network from my other devices via iCloud Keychain. So even though I've forced my iPad to "forget" the 5GHz network, it still occasionally connects to it and I have to manually change back. Annoyingly, when I forget the 5GHz network, the password is removed from my keychain, so I have to re-enter it on other devices.
I haven't read every post above but it does seem that this issue is highly correlated with the BT Home Hub 5. Of course, the fact that other devices still work properly with this router suggests that it's not solely a router problem. It seems likely to me that this issue is caused by some weird combination of parameters between the iPad and this particular router (at the hardware, firmware, or software levels). Has anyone been able to replicate this exact issue on a different router?