I'm having the same problem. Here are some more details...
I have tried initiating Bluetooth pairing from System Preferences on my Mac, and also initiating it in Preferences on my iPhone. This does not seem to make any difference. I have also tried the exact procedure described in the FAQ where I removed the devices on both, shut down Bluetooth on both, and started fresh. The pairing is not a problem at all, just the reconnecting after the devices are already paired, and the problem seems to be with Type2Phone recognizing that the connection has been made.
I expect to open Type2Phone, click to connect (or in my case, automatic reconnection on launch), and moments later be able to use my MacBook Pro keyboard to type on my iPhone.
What happens instead is I open Type2Phone, click to connect, and it says "Connecting..." until I see "Connection failed." During this process, I see Hardware Growler (another app) tell me that my iPhone has connected via Bluetooth, but Type2Phone doesn't seem to recognize this. Then, a while later, Hardware Growler tells me my iPhone Bluetooth connection is disconnected, just before Type2Phone reports a connection failure.
If I have Type2Phone open and I go into the Bluetooth settings on my iPhone, I can tap my MacBook Pro's name in the list, and a connection is made properly every time in just a few moments. I don't have to do anything with my MacBook Pro; I just open Type2Phone and tap my computer in the iPhone's Bluetooth settings.
Although effective, this is not very convenient. I want to connect a keyboard to my phone for whatever I am doing at the time. I do not want to have to switch the phone to the settings app in order to make a connection. This morning, for example, I wanted to control the music playing on my iPhone, which was in the next room. Instead, I had to go to the phone to make the connection work, and at that point it was easier to just control the music from the iPhone, not my computer using Type2Phone.
Anyway, that's what I know. It's not a problem with pairing, although re-pairing will make a successful connection. It's some sort of problem with how the connection is handled on subsequent attempts.