I have just solved the problem.
Windows 8 stopped detecting my external monitor as soon as I changed in the VM Settings | Options | Guest Operating System | Version
from Windows 7x64 to Windows 8x64.
All I had to do was to revert this setting to Windows 7x64 and all works fine again.
It seems to me that there still may be a bug in VMWare Workstation 9 when it comes to full support of Windows 8 x64 operating system.
Questions closed. I may open a problem report for them if I find out how to do that.
Andrew
P.S.
Could someone help me to submit a problem report to VMWare?
Thanks in advance