Thank you @A_Wyn_Jones for you helpful insights.
To our findings we tried following your suggestions and observed that the server machine fails to connect to https://Datastoremachine.domain:2443/arcgis/datastore.
This works well in datastore machine for both localhost and domain URL.
There is one additional info that I think is quite suspicious. We are using NLB URLs configured on top of our web adaptor URLs for accessing server and portal, and those were configured before installing and registering datastore machines with the server.
Can this could be a possible trigger for this issue? Or should we focus on why this domain URL fails to communicate from the server machine?
Adding some more info from the describedatastore.bat utility we observed that the machine with relational datastore's owning system URL is web adaptor URL whereas the other machine with tile cache datastore shows Port URL.
We have 2 datastores installed on separate machines, and the issue with errors/logs is in relational.