So after days of trying to get a small, off-brand, bluetooth keyboard up and working on my RPi3, I finally gave up and sent the keyboard back. I went out and found a name brand bluetooth keyboard, an HP Bluetooth Keyboard K4000, and set it up. I had about 30 seconds of use before I started getting the same results as the off-brand keyboard - namely the thing won't stay connected. I have had no problems with my Logitech M557 bluetooth mouse. Here's what I'm seeing. Any thoughts?
[bluetooth]# connect 08:B7:38:14:D4:3F
Attempting to connect to 08:B7:38:14:D4:3F
Failed to connect: org.bluez.Error.Failed
[CHG] Device 08:B7:38:14:D4:3F Class: 0x000540
[CHG] Device 08:B7:38:14:D4:3F Icon: input-keyboard
[CHG] Device 08:B7:38:14:D4:3F Connected: yes
[CHG] Device 08:B7:38:14:D4:3F Connected: no
[CHG] Device 08:B7:38:14:D4:3F Connected: yes
[CHG] Device 08:B7:38:14:D4:3F Connected: no
[CHG] Device 08:B7:38:14:D4:3F Connected: yes
[CHG] Device 08:B7:38:14:D4:3F Connected: no
[CHG] Device 08:B7:38:14:D4:3F Connected: yes
[CHG] Device 08:B7:38:14:D4:3F Connected: no
[CHG] Device 08:B7:38:14:D4:3F Connected: yes
[CHG] Device 08:B7:38:14:D4:3F Connected: no