Bluetooth periodically stops working on iPhone 6s Plus

I've been having a problem with my iPhone 6s Plus since I got it on launch day. I've tried doing a restore and also upgrading to iOS 9.0.2 and continue to have the following problem.

Periodically and seemingly randomly, Bluetooth just stops working. I can't pair any new devices nor connect to existing paired devices. All handover and continuity functionality stops working. Basically Bluetooth just doesn't work. At the same time I lose the ability to see any 2.4 GHz WiFi networks. 5 Ghz WiFi continues to work, but not 2.4 Ghz.

When this is happening, if I turn Bluetooth off, the 2.4 Ghz WiFi networks suddenly start showing up and working. That makes me believe Bluetooth, which also uses 2.4 Ghz, is somehow tying up or jamming the 2.4 Ghz radio.

I can then turn Bluetooth back on and everything works until the problem starts happening again. Turning the phone off and on also fixes the problem, but toggling Bluetooth is faster

I've seen this problem 4 times in 6 days and in those 6 days, I've done 2 restores, 1 iOS upgrade and a number of phone restarts, all which would correct the problem temporarily. I've never seen the problem on my iPad Air 2 or iPhone 5s, which are also running iOS 9.0.2.

Anyone else having this problem? I feel it's a software problem and not a hardware one since toggling Bluetooth fixes it, but I don't know for sure.