Ive had this problem in the past and it is a power setting that causes this issue.
These steps should sort out your problem;
The screensaver comes on for awhile and then goes blank.
This probably means that the power settings of your monitor are set to turn off the monitor at the same time or even before the screensaver is started.
How to fix this:
Go to the the screen saver tab of the display properties (found in the windows settings control panel)
In the screensaver section you will see a "Wait" entry box. This is where you time the amount of time after which, the screensaver will start. Set this to 3 minutes.
Lower, you will see the "Monitor Power" section. Hit the Power button to change the power saving settings of your monitor.
In the "Turn off monitor" entry box, put a value that is greater than the "wait" value that you have put in the screensaver. Eg. 10 minutes.
The next time you leave the computer without keyboard or mouse activity, the screensaver will start after 3 minutes and the power of the screen will be cut after 10 minutes. That will allow the screensaver to play for 7 minutes.
Try the above and see how you get along.