Why does my battery drain while sitting?

You said there is "no detectable parasitic drain". But you're also saying that the battery immediately begins draining when you connect the grounding cable. It's kind of a contradiction. If the battery appears to be draining with the engine off and cable connected, then you'll have to determine what is pulling the power, and perform needed diagnostic testing in the related circuit to figure out why. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops