That may be the biggest gripe people have with bluetooth input devices. That once asleep, it takes noticeable time before it wakes back up and during that time all inputs are /dev/null-ed.
On Linux, it does this.
On OSX, however, it still takes a few seconds to wake up, but the keystrokes typed while 'waking up' do make it through to the screen in the right place.
I keep meaning to dig into the Linux Bluetooth stack to see if those initial keystrokes can be salvaged. I guess they're sent in a burst once the keyboard realises 'yeah, I'm being typed at', but Linux seems to ignore them for some reason.
It also costs 10x as much as the regular BT buttons. Can't wait for BLE to drop to mass market prices.
For now, you can always buy your own bluetooth LE modules and attach them to a small microcontroller, for buttons, you could make your own wall buttons with nice enclosures or go the ridiculous route: https://www.adafruit.com/products/1185
https://www.stavros.io/posts/emergency-food-button/
A bit latent, but doesn't require a second press.
I definitely recommend it, KiCad is great, the people at #kicad are great, and the people at https://gitter.im/esp8266/Arduino have taught me most the little I know now. I can't urge you enough to try it.