rocklobster knows what's up.
That's why you see sprinklers set up on new concrete... often new parks (especially if the weather's warm when they pour) will be kept wet for awhile before you can skate them.
Time is also a factor in curing; people don't park cars on a new driveway for a few days... ideally you wouldn't skate your new ledge for a few weeks. Concrete actually cures for a long time before it's done.
Also, do you use an edging trowel? You don't want a sharp edge, since concrete is brittle when it's thin. If you slightly round the edge with an edging trowel, that will help with chipping/crumbling. I'm not talking skatepark coping-round, just making sure it isn't sharp.
One more thing: I'm assuming you're mixing your own concrete and not ordering it from a ready-mix company. If so, you probably aren't vibrating the mix. Next best thing is to tap the forms all around with a hammer to get all the air to bubble out. If you don't, you'll be left with air pocket voids when it sets. Obviously this would be bad near the top edge that you're going to grind.