I have had this problem with a Truvativ Elita crank. Tall gear, stand to accelerate, and it drops, even with the FD adjusted within a hair of the chain.
I took it in, and was told that the crank spider was coming loose from the axle. I hadn't even put 500 miles on the bike (CAAD8), so they warrantied it. I chose a Shimano 105 compact as a replacement, and it hasn't dropped a chain in 1500+ miles.
Your Rival crank appears to have the same construction, so I'd consider using a different crank. I'd even keep my Shimano crank if I changed to SRAM shifters.