We have both models at our house and their bluetooth abilities are very different. Different Bluetooth chip generations and different bluetooth protocol versions. With the older battery powered keyboard, my experience over the years has been...
  1. Be sure the batteries are fresh when pairing
  2. Don't use rechargeable batteries — their output voltage is a little lower and that can make a difference, especially when pairing the keyboard
  3. Don't use cheap batteries — stick to the major brands
  4. UNpair the keyboard from ALL other devices before attempting to pair it with a new device. (This can be tricky if the other device is no longer around)
  5. Other bluetooth devices within a radius of 30 feet or so can cause problems when pairing. Turn them off or move them further away until the keyboard is paired (I can't verify cause and effect, but In one case I was wasn't successful until I powered a nearby 2.4GHz band WiFi router down)
  6. I can verify this, the bluetooth chips and firmware version in the newer "Magic" Keyboard, trackpad, and mouse pairs automatically, is longer ranged, and more stable. (Their built-in Lithium batteries go a long time without recharging too.)
Hopefully one of these will help. My one remaining battery powered wireless keyboard is on my wife's computer and although she will accept software change with only a little little to no grumbling she will NOT let me switch her keyboard out because, "might feel different" and she will not try mine out to see. (Admittedly It does have a different touch smile )

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein