I would check the insulation as you suggested. Also check to see that there are no holes in the hose or that the connections are tight. Another option is to install a rigid duct or pipe to set the line in a draining outside dirrection. Sometimes the flex line are just drooping and do not get rid of the water , then find a spot to leak. You only need a pin hole and a drooping line to have water stains.
How long is the run of pipe, if it is over 8 feet you may need a larger capacity fan.
Let us know.