I have a BlockBreaker set up like this - to be a cobble gen on a FTB Infinity Evolved: Expert Mode Skyblock world:

http://i.imgur.com/Sy2mOLz.png

While the screenshot shows evidence of it operating, after breaking a few hundred cobble it will stop, until I cycle the redstone signal.
This happens both on SSP, and playing on a craftbukkit server.

This happens when the next stone forms too quickly and the breaker never has a chance to 'reset' before getting the next signal. This is just how the breaker works. You need to make your cobble gen differently.

And yet the OpenBlocks block breaker, setup identically, works just fine. Although I am intrigued how one would "make a cobble gen differently" in a way that could fix this: you pretty much always have lava flowing into a space adjacent to water.