Strange Kitchen Sink Problem

I have a double kitchen sink in my fifth wheel. If I run water in the sink it will not drain. I have let it sit a couple days and I look and the water is gone. If I run water again, it will not drain out. I have tried everything for sink clogs, used a snake and nothing happens or changes.

Has anyone run across this before? The sink is either clogged or it isn't, so why does it suddenly drain all the water out?

I need my sink back! Any ideas?

As a side note, my bathroom sink and shower drain fine.