Isn't this something
you should be discussing with your company's IT department?
There are far too many unknowns for me to be able to help you in any way with this. What is your company's VPN server? How is it configured? Network topology? Firewalls? Remote Desktop server? VPN client on your machine? Remote Desktop client? Configurations of each of these? And many many more...
I'm not asking you to answer any of these questions, I'm just pointing out that any one of these things could affect the stability of your connection and we have no way of knowing which of these it is. Even for you to say that it is the upgrade from one version of OS X to another is the cause may not be the case as some other thing may have changed on your company network without your knowledge.
My advice is to take this up with your IT department. After all, it is their responsibility to keep these things running smoothly.