When my lunchbox planer had that problem, it needed a good cleaning. There's probably a chain mechanism to keep the movements up and down both post in synch. Mine is in the bottom of the machine, have to turn it upside down to access the plate that covers it. A good cleaning with an old toothbrush and some WD40, then some spray lube did the job.
Also make sure no crud has accumulated along the posts and that the springs are not broken.
Let us know how it comes out!