I've only tested out a few different Bluetooth devices, but I haven't seen any disconnect on button presses. The Kobo software does have a pretty aggressive timeout (150 seconds) for Bluetooth though.
In case you don't have any luck with whatever built-in support exists, I've written a plugin for using arbitrary Bluetooth devices to turn pages on Bluetooth-enabled Kobo devices. There's a thread here:
https://www.mobileread.com/forums/sh...d.php?t=345507