Just moved from a Galaxy S3 to an S4, and I am seeing this issue, where I had no issue on the S3. It's as if the bluetooth radio goes into some low power mode. If I move the phone closer to the headset, reception improves. I was thinking I needed to update the radio in this phone, but reading your responses, that does not seem to be the issue.
Phone #1: Samsung Galaxy S5 Active
Phone #2: Samsung Galaxy SIII
ROM: Task650 AOKP
Recovery: CWM Touch
Retired: Samsung Galaxy S4, Motorola Droid 3, HTC Vision G2, OG HTC G1