Are they ripped, cracked or dry rotted? Dry rotted canvases will appear to weaken and tear for no real reason. Are they painted with latex, or dyes?

Your best bet is to glue a similar patch of canvas to the canvas from behind.

1.)You will want to cut the patch at least a couple of inches bigger than the area to repair.
2.)Prepare the canvas patch (size it if the backdrop is sized).   
3.)Lay the canvas to be repaired face-down on a clean, flat, dry surface.
4.)Clean the back of the area to be repaired.
5.)Apply a thin even layer of flexible glue (white glue, tacky craft glue, acrylic gesso or medium) to the patch and to the repair area. Don't apply thickly.
6.)Position the patch and weight it in place.
7.)Allow to dry.

Test the patch to make sure it is solid.

Less correct solutions can be used if the backdrop is at the end of its useful life or less valuable or as an emergency fix. These less correct solutions include duct tape applied from behind. Or a patch applied with hot glue from behind.