Which version of Outlook?
Does this problem only occur when you are using your VPN connection?
When you try to send mail, are you connecting to the company to do so, e.g. and Exchange server, or a commercial ISP?
Have you tried setting up an alternative email account (e.g. Yahoo, or one of the many free POP3 email accounts that Google will locate for you). This will help isolate whether the problem is at your end (within Outlook, or within your network configuration), or within the receivng end (your workplace server).
Have you checked within Event Viewer for error messages?