SPS13 "Open with Explorer" random error "We're having a problem opening this location in File Explorer. Add this web site to your Trusted Sites list and try again"

In a SharePoint Server 2013 environment, (on this case with Windows Server 2012, and Windows 7 Ent SP1 client machines  with IE10), you may face the following situation:

When browsing a document library with some folders and sub-folders, you may attempt to open them with the "Open with Explorer" ribbon command.
In general it t works, but as you continue to browse folders and open with Explorer, at random intervals (after ~ 5,6,7 or 8 times) you may face the error:
"We're having a problem opening this location in File Explorer. Add this web site to your Trusted Sites list and try again".

The error is random and occurs after a few user actions (i.e. browse a folder, open with explorer, close, then open another folder, open with explorer, etc.).
The issue is resolved, when IE is re-opened, until it occurs again after a few tries...

The cause and the resolution methods are the following:

Cause: There is a missing Root site collection...
Resolution: Check and ensure,  that the “Managed Paths” are not changed in the web Application’s page, there is a (root) explicit for this web application and there is a working Root site collection.

If for any reason this is not the case in your environment, you may try the following:

- Apply (if not already) the following Hotfix to one of those clients:
Error when you open a SharePoint Document Library in Windows Explorer or map a network drive to the library after you install Internet Explorer 10 in Windows 7 or Windows Server 2008 R2
https://support.microsoft.com/kb/2846960
Then, try to delete the cache of the IE browser before reproducing the issue. Check the result..
- Try to temporarily disable the Antivirus and test again.
- Check if you have installed the Desktop Experience feature on the SPS13 server.
- Check if you face this behavior with all users, Or only with some specific ones, Or with all different client OSes.. 
Otherwise you will need to collect the logs to further analyze...