Bluetooth Headset "failure"?

[EWyatt]

My iPhone 4 works perfectly.... so when I purchased a bluetooth headset today, I thought all would be well. However, after pairing up the iPhone and the Bluetooth device and after making a couple of successful phone calls, all seemed good. However, the headset (earpiece) loses pairing with the iPhone after several minutes of non-use. Is this normal? Aren't these Bluetooth devices supposed to be "connected" to the iPhone until they're shut off? Does the iPhone have an option for disconnecting the Bluetooth device after a certain period?
Sorry for the questions. The Bluetooth device has practically no users manual. Perhaps I just got a bad Bluetooth device -- it was cheap!