Hi RahulKapoor,
Thank you for reaching Microsoft Community and apologies for the inconvenience this has caused you considering that this had been going on for a long time already.
May I know the exact model of the Asus monitor that you are using?
are you using a directly mini-DisplayPort to DisplayPort cable in connecting the monitor to the dock or an adapter is being used in between? Is it a passive or an active adapter?
How about if the monitor is connected directly to the mini-DisplayPort of the Surface Pro 6, does the same behavior also occurs? This is for us to isolate further if the issue is caused the by the Surface Dock or the on the Surface Pro 6 itself.
Also when you wake the device up and issue occurs, please try to press Windows key + CTRL + Shift + B to reinitiate the display driver of the device and see if it automatically fixes the issue.
Please try also updating the dock again using the Surface_Dock_FwUpdate_1.53.139_Win10_17763_20.075.41193_0_AMD64.msi file (see; Microsoft Surface Dock 1 Firmware Update - Surface | Microsoft Docs) and see if it helps.
I'd love to provide you with the troubleshooting steps right now to fix the problem. I am afraid that we may have to wait for the above answer first so that we can provide the necessary information. Once we collect all the information, we will formulate the feasible resolution to help you with your case or if we need you to refer to the support that suits your problem.
Kind regards,
Marrion