Sometimes when you pop up early you are in fact 'too early' and then stuck on the top of the wave (which then collapses underneath you) rather than just under the lip (ie just forward of the top of the wave) which is where you want to be. Particularly on small waves, there may not be enough power in the wave to get you down the face (without you doing some speed movements, like pumping).
This is just a timing issue - now that you recognise it and are getting 'the feeling', when you think you want to pop up take another stroke (or two) then pop up. This is the scary part in a way, because by this stage the board is probably already pointing downwards a bit. Look at that video right on 2.02 - here is a screen cap, showing the perfect spot to take off and that the board is sort of heading downwards already (but because of the size of the wave he could take it at an angle which minimises the downward ness)
And lean forward as the others say, try to scream down that face not go down as slow as possible.
I hadnt seen that clip before - should show it to those who claim being on a longboard is holding them back and they need a 5ft8 shortboard ASAP to make any progress.