this may sound odd but here goes...
When was teh last time you cleaned and resealed your roof membrane?
I clean and seal mine first thing in the spring and once again about late August.
We try not to park under sap bearing trees when on the road and at our seasonal we don't have any trees hanging over our unit.
The black streaks are coming off the dirt on teh roof (makes sense that if you haven't cleaned it at least once a year...)
We use Camco roof cleaner and resealer as well as the Camco black streak remover to get the job completed. We also have changed our short gutter spouts for the ones with the extensions.
if you have short spouts, try clipping a wooden cloths pin onto the spout. It lets the roof rain water clear the side of the trailer.
2009 Heartland Sundance 31.5 XLT bunkhouse
2013 Ford F150 XTR ECOBOOST
"Of the troops - For the troops "