Finally I can see messages in OVI suite 2.2.1.23 under Vista 32.

How I made it?
Because I didn't know what was causing issue, I decided to remove all Nokia's components from my PC. I used Revo Uninstaller 1.90 (freeware) for that. First in Revo's search box I typed word "Nokia" to see just Nokia's applications/drivers. Then I uninstall them one by one in Advanced mode (to delete all files and registry entries). After that I rebooted my PC and installed OVI Suite (requires another reboot to complete installation). Now OVI Suite is showing all my messages.

EDIT: Also messaging is working in PC Suite 7.1.51.0