When the graphics card starts sending signals, it tells the monitor to start running. When the monitor is getting this signal it is shutting down instead of starting up. When you are powering off and on again you are bypassing the signal stage.
I think it may be a fault with the monitor (it may even be a safety cut-off). You can probably only tell by using a different monitor to check that the problem is not in the graphics card.
If the problem is in the monitor and it is still under warranty, you should have it repaired before the warranty runs out.
See if you can spot the problem listed here (don't try repairing anything inside the monitor yourself) : http://www.repairfaq.org/sam/monfaq.htm