I have a quilt using a rod like you have. I used 3M Command Strip hangers on the ends to hang the rod. The quilt hangs on a wall that is next to our bedroom and the DVD movies that we have are also stored next to it. So it sees LOTS of bodies walking by and stand next to it. I am sure it has been touch and pushed just a few time
Not once has it falling off!! Bonus on my part, no holes in the wall since we are living in a rental!!