if it is a network drive mapping issue, try using Resco File Explorer while connected to VPN and see if that will allow you to remain connected.
Sorry for the questions and additional troubleshooting, but no where in this post have you really outlined that the drive mapping was your main concern.
Also I found a useful post that was a bit old, but maybe of some use. The Windows File Explorer and IE have a registry entry that have a hard max # of connections allowed. I had similar problems with certain web pages, until I fixed this entry. I will edit this post when I find the link.
Here you go:
http://www.ppcgeeks.com/increase-max...uot-t1365.html