try changing the wireless in the hub from default b/g/n to just b/g.
This might not be applicable but it may give you a clue as to what to check.
1, i just received a new HH3 today and I logged on straight away with my ipad on the default settings.
2, I changed the network name to one i used previously on my HH2 and that was where my problems started. I went back to my ipad and tried to log on to the new network but it wouldn't. A bit of head scartching and i realised that BT wanted me to increase my security on my HH3 so I had changed the password. My ipad however was just seeing the network and trying to connect with the old password rather than asking for the the new passwod.
3, I told the ipad to forget the network, reconnected and everything is now fine.
If your ipad/iphone isn't asking for the key it obviously recognises the network and is trying to connect with an old key, which is probably why you can connect with no security.
I have similar issue with ipad2 both ios4 & ios5, wireless connection to hub3 drops out repeatedly. Have tried forget network and start again, and problem persists.
I'm not sure whether you managed to fix your problem but I have been experiencing the same issues over the past week and changing the security etc didn't work for me.
I found the fix for me was to delete the connections from my iPad as previously mentioned and then go into the Wireless settings via the HomeHub page and Advanced and change the physical SSID name. Once this had been changed and accepted I reconnected my iPad and found I had the normal WiFi download speed. I'm not sure how long this will last as I only made the change today but so far it's been good (I was previously trying to watch Endeavour via ITV Player and the connection just kept dropping but this afternoon I watched the program without any hitches).
I have had this problem connecting iPad, iPhones and Blackberry to a BT HH3 installed as a replacement for an earlier generation hub.
All the other devices in the home connected by ethernet operated correctly.
Macbook and iMacs connected without problem using the wireless key.
Drove me nuts ... Apple recommend resetting wireless settings in the devices
Reset network settings
To reset your network settings, tap Settings > General, then tap Reset > Reset Network Settings.
When the device restarts, try to locate and join the Wi-Fi network again.