Problem with one Braille display and multiple Apple devices.

Hi guys! :)
I've had an iPhone for over a year now, and I use it quite a fair bit in conjunction with my Braille-Sense U2, as both a Braille display and a keyboard. Now a few days ago I got an iPad, and I'd really like to use it with the Braille-Sense as well.
However, as soon as I paired them, I'm running into quite an inconvenient and annoying problem. Whenever I'm using one device with the Braille-Sense, and the other one happens to for example receive a notification in the meantime, I believe it makes the poor Braille-Sense go nuts and it no longer knows with which one it's supposed to work. The result is that it pretty much stops working altogether, in that when I'm in the terminal mode the keyboard becomes useless and it's no longer possible to type anything with it or navigate the screen of the device that I've initially connected it to. It will still be able to display whatever's going on on the device, with a very noticeable lag. The only way so far that I've found to get rid of the problem for the time being is simply locking and unlocking the device. It's really quite frustrating though having to lock and unlock it regularly while I'm trying to do something and I'd like to be able to fix this problem more permanently if it's possible.
Has anyone ever come across something like this with a Braille display and/or knows how to fix/work around such a thing more effectively? I'm pretty sure I've heard before of people who use one display for multiple Apple devices but perhaps the Braille-Sense isn't among the ones that are fit for it or I'm doing something wrong?
Don't know if that could be relevant, but I'll mention in case it might, that I had some issues when pairing the iPad with the Braille-Sense so it took quite a couple attempts, and then my sister unintentionally made the iPad forget the Braille-Sense so they had to be paired all over again.
Will be very grateful for some help with this. :)