After reading tons of suggestions and solutions (even disabling PCIe sleep mode) while "Monitor Deep Sleep" option doesn't exist on my monitor model, Dell S2721DGFA. In my case the problem was solved by doing the following =

* Enter the Menu OSD (page 44 in the online S2721DGFA User's Guide)
* Go to Input Source
* Select DP
* Change Auto Select from On to Off
* Exit the Menu OSD

I hope this simple way solves the problem for other users as well