Yes. Totally having this problem.
I filed Radar 21964253 about this. Feel free to dup. http://openradar.appspot.com/21964253
Some examples from my device logs:
# BTLEServer dies:
Jul 23 10:41:17 MyiPhone BTLEServer[153] <Error>: (Error) Received unexpected end of input stream on pipe <CBScalablePipe: 0x13c50efa0 peer = <CBPeer: 0x13c50eff0>, name = "com.apple.BTLEServer.classic", type = server, priority = high>
Jul 23 10:41:17 MyiPhone wirelessproxd[64] <Notice>: (Error) identityservicesd's WPDContinuity connection died
Jul 23 10:41:17 MyiPhone wirelessproxd[64] <Notice>: (Error) identityservicesd's WPDContinuity connection died
# BTLEServer tries to come back up:
Jul 23 10:42:16 MyiPhone nanoregistryd[95] <Warning>: 07-23-2015 10:42:16.918: -[NRRemoteObject service:devicesChanged:] com.apple.private.alloy.bluetoothregistryclassc: decided we're ready
Jul 23 10:42:16 MyiPhone nanoregistryd[95] <Warning>: 07-23-2015 10:42:16.921: -[NRRemoteObject service:devicesChanged:] com.apple.private.alloy.bluetoothregistry: decided we're ready
# BTLEServer dies:
Jul 23 10:42:32 MyiPhone wirelessproxd[64] <Notice>: (Error) identityservicesd's WPDContinuity connection died
Jul 23 10:42:32 MyiPhone BTLEServer[153] <Error>: (Error) Received unexpected end of input stream on pipe <CBScalablePipe: 0x13c605c50 peer = <CBPeer: 0x13c61f3f0>, name = "com.apple.BTLEServer.classic", type = server, priority = high>
# BTLEServer comes back up and connects to watch:
Jul 23 10:42:55 MyiPhone companion_proxy[252] <Notice>: CompanionProxy: -[CPXService checkNearbyDevices:]:107 (0x0x16e113000): nearbyState changed to 1 for 71f5300df6004bbc9d84eef00e
Jul 23 10:42:55 MyiPhone companion_proxy[252] <Notice>: CompanionProxy: -[CPXService checkNearbyDevices:]:129 (0x0x16e113000): Enabling BT Classic