since it seems that you are not starting your animation with the cloth directly against the cylinder, Im thinking perhaps you should be using a choriographed and not a constrained group. set the cloth to collide with both the cylinder and the ground than set the row of vertexes that you wish to stick to the cylinder to be a choriographed group, start the cloth in frame 1 where you want it to fall from. than decide what frame that you think the cloth should come in contact with the cylinder, and in that frame move it to just about touching the cylinder, making sure that your choriographed vertexes are lined up with the cylinder than run your simulation allowing enough frames after your second key frame to let the cloth drape the way you want.