I had a problem, may take a screen shot.
I added an extra escape path to my depot room, raised the bridge over a ditch in the path... and then my depot apparently became inaccessible.
Has anyone else had problems with multiple paths to their depots?
Having multiple paths to/from your depot is no problem, as long as at least one is open at all times. Having multiple depots will cause problems.
As for where the problem is, remember that the path moves out from the depot to the edge of the map. As such just turn on the accessibility screen, and then follow the green tiles out from your depot until they stop, which will show you where the problem is. Remember that trees and "boulders" (the kind you find attached to the floor aboveground, not the item) will prevent caravans from crossing over them.