Looks like you don’t have much chain wrap on that center sprocket. That could cause it to skip teeth when you have a lot of resistance.
What you can’t see is an idler hidden by the top frame rail that wraps the chain more around the top in addition to what you see of the bottom of the sprocket . Almost 50 percent of the sprocket’s teeth are in contact with the chain. The final drive ratio is 22:1 and it can push rather nicely.
Judging from the picture, there is only about 45 degrees worth of chain wrap around that center sprocket. At the very least, you should always have at least 180 degrees of chain wrap around a sprocket. In a high torque application such as a drivetrain, you’re much more likely to skip teeth on the sprocket if you do not have adequate wrap of the sprocket. 
I have just one question,
does the chain touch on the top and the bottom of the sprocket or does it wrap around it? If it touches in two places you may want to be weary of the chain breaking, jumping, falling off, or simply stretching so it doesn’t nicely touch
just my first reactions,
-Dan
Dan and Gus you’re both right. Yes, the chain meshes on both sides of the sprocket and the sprocket on the transmission is in the position of the second idler Gus shows. There is no chain/sprocket contact that is less than 120 deg of circumference. In fact both end sprockets are almost 240 deg. We played around with many designs for a single chain six wheel drive during the off season and this one is the one that met our requirements (reliable, durable, and simple). We’ve run it and this design seems to be nuke proof. However, the true test will be on the field with other robots.