Yes actually I did. I've been on 4.3 for a while now so I haven't noticed it lately, but when I first switched I noticed it. I believe you've got to turn up the volume in the phone to fix it again. It's like the phone defaults to a lower bt volume even though you've got it turned all the way up in normal speaker mode.
Exact same problem with my HTC and 4.3. Bluetooth connects then drops every 10-15 seconds. This is ridiculous. I thought the new retarded Google maps was bad, but not having functional BT is wrong. Never had a problem before 4.3.
Have spoken to HTC they have not acknowledged it as being a software related issue. They have advised me to arrange a repair for the phone! Looking at various sites it seems that 4.3 is the issue when it comes to Bluetooth compatibility.
HTC won't acknowledge anything. They think it's user error. We have 3 cars that I've tried to pair BT to. It does not work. It worked fine on Android 4.2.
i've owned the HTC for a month now and found every time i restore to factory settings the bluetooth works for a day. not long i must admit but i believe its to do with the automatic updates so will attempt to disabling the automatic updates and seeing if this works the weekend.