Hi Mike W.
I believe the blurb says that in Receive mode i.e Rx it does power down after a set time but NOT in Transmission Tx mode and that's the mode I use as I wan't to listen via BT headphones.
I don't use mine permanently powered but instead using its internal battery.
As regards pairing, when I had it I initially connected it to the Brennan using the Analogue jack lead supplied and after switching on my headphones and then the Blitzwolf it seemed to pair within a few seconds.
I now have it connected via the Optical cable and the pairing each time is a bit iffy but I turn on my headphones and the blue light on the phones flash and then I turn on the BR4 and after a few seconds it flashes rapidly and may pair and perhaps another push of its silver button does make the connection. If that does not work then i turn off the phones and then back on but this time in its pairing mode and hey presto!
I should say that currently I am awaiting a replacement free of charge BR4 from Blitzwolf as I have been experiencing a lot of audio dropouts which of course may not have anything to do with the BR4 but they have been gracious enough in offering another one to try. There are so many other things in my house that could interfere as they operate on the same 2.4Ghz waveband.
I've even contemplated buying a very cheap Bluetooth speaker to see whether there are dropouts when listening via that as after all it could be my 'cheap' Mixcyder E7 headphones that are at fault.