I have a Viewsonic VP2130b 21" LCD, which sits in my warm comfortable study (so I know that temperature is not an issue). Now and then, it too fails to turn on during restarts, activations from sleep and so on. It is a sporadic problem, and I have worked out a solution that always recovers it, and so I put up with it, since it is such an excellent monitor (clearest, brightest, best image I have ever seen). I have always assumed that Viewsonic had a bit of a compatibility issue with Apple. I am surprised to see this happening with Apple monitors! They ought to work with Apple computers!
In case it may help, here is the solution I use. It works every time, and it is just a matter of timing. Two cases need to be considered:
Cold Power On of the Mac. I start with the Mac and the monitor both fully off. Power on the Mac itself, and wait for the startup chime. Once you hear the chime, power on the monitor main switch and then turn on the front panel power switch. Thats it - it has never failed.
Warm Power On of the Mac. In this case, the Mac has been previously running and I have told it to sleep. I am now "waking it up". The monitor is in standby mode at this point. 90% of the time waking up works as expected and everything comes up, no muss no fuss. When it doesn't, the Mac seems to come up just fine but the display never turns on. In this case, I put the Mac through a restart and apply the "Cold Power Up" recipe from above.
To do this, I use the key combination CTL+CMD+EJECT (EJECT is the CD/DVD tray open/close button) to force an immediate shutdown and restart. When I hear the machine reset to ROM (I can hear the CD/DVD drive make a characteristic noise at this point) I turn off the monitor. Then I wait for the reset chime and turn it back on. This seems to ensure that the monitor comes on every time.
This is a really silly workaround, and I have no idea what the root problem is, but it has saved me from the experience you are having, where you have to restart over and over and over, waiting for that random combination of conditions to be just right, so that the Mac and monitor recognize each other and all is well. This is a one-cycle, never-fails workaround. It is annoying but effective. I hope that it may work for you!
Good luck!