Moto G in to USB Debugging mode issues on Windows 7
I tried with a different USB Cable and it is working stable now. 

Unfortunately Moto G doesn't come with USB cable as part of the accessories and hence we have to rely on the USB cables available in the outside market.

Currently I'm using Sony Xperia's USB cable which is working like a charm on my Moto G for USB Debugging. It's been couple of hours and the USB debugging is still on and going great :)

Let me observe the same for another day before I conclude the issue. 

And another suggestion I received is - Do not work on Windows for Android Development but stick with Linux as windows drivers are buggy in most of the times.

I appreciate the suggestion as of now and may look at this option as well in the near future to switch to Linux for Android Development.