When you say "connect" what exactly are you trying to achieve?
Airdrop? Mobile Internet Hotspot? Airdrop?
Which Mac, iMac, MBP, MBPA do you have?
To cut a few things short, and to save you time. The only connection you'll ever establish between your iDevice and you Mac is purely for internet purposes. ie.. if you're out of reach from wi-fi connection, you can use your iPhone as an internet connection (provided that you have data bundled in with your mobile contract).
The new features, which are dubbed "Bluetooth 4.0 LE" (low energy), don't stay connected. They merely make connection as and when needed (hence why they're dubbed low energy).
If this doesn't help, give us a shout, let us know what you've got (as I asked before) and we'll try help :)