Update:
Asus bluetooth dongle does not solve my problem. It also disconnect randomly, however less often. And here is what happened:
default 04:10:35.283774 -0700 locationd {"msg":"kCLConnectionMessageWatchdog", "event":"activity", "this":"0x7fc878f61fd0", "registrationRequired":0, "registrationReceived":1}
default 04:10:36.707045 -0700 kernel [IOBluetoothHostController][ProcessEventDataWL] -- Bluetooth Firmware Error!! Not enough data to be a valid LE Advertising Report
default 04:10:40.996040 -0700 kernel **** [IOBluetoothHostControllerUSBTransport][terminateWL] -- entering -- mCurrentInternalPowerState = ON -- this = 0xc800 ****
default 04:10:40.996165 -0700 coreaudiod hostController general interest notification e0020009
default 04:10:40.996251 -0700 coreaudiod PowerState:1 bluetoothdXPCConnection:0x7fa48fc2b980
default 04:10:41.002662 -0700 bluetoothd INIT -- Host controller terminated
default 04:10:41.002692 -0700 bluetoothd Host controller terminated
default 04:10:41.002722 -0700 bluetoothd -[CBXPCManager hostControllerTerminated]
default 04:10:41.002742 -0700 bluetoothd -[CBXPCManager hostControllerNotReady]
default 04:10:41.002760 -0700 bluetoothd -[CBXPCManager hostControllerNotReady]
default 04:10:41.002788 -0700 bluetoothd -[CBPowerManager updatePowerState:] - New State:0
default 04:10:41.002813 -0700 bluetoothd -[CBPowerManager updateClient:] - Central (0) UserEventAgent:320
default 04:10:41.003055 -0700 bluetoothd -[CBPowerManager updateClient:] - Central (0) wirelessproxd:350
OSX terminated the bluetooth host controller, because it could not determine that it supports LE - I think.
I have moved on, I purchased a set of Logitech wireless keyboard and mouse that works with Logitech Unifying USB controller (not bluetooth).
However, I am disappointed with Apple, cause they have the advantage of building their own hardware platform and better control over software/drivers for hardware peripheral, and yet this could happen.
I have now read so much about Mac bluetooth issues that I will be caution about getting my next iMac. Lucky for me that my Mac Mini and Macbook Pro does not have this problem.