No slippage so far. The fact that I used 6" board and made a tight fit to my sink of the blocks on the underside keeps it in place across the sink really well. I mostly use a wet handi-wipe on the board under the stone and it's been really solid for me so far.
Like I said, I make garden beds and I use the 6" cedar for them so a big part of it was that I happened to have it on hand as scrap. 2x4 or 2x6 would work too.