Locate a patch kit that is designed to repair a velour air mattress. These kits are available at many camping supply stores or can be ordered through the mattress's manufacturer.
Inspect the air mattress to locate the source of the leak. If the leak is not visible to the naked eye, apply a layer of soapy water to the mattress with a paintbrush. The soapy water will bubble at the site of the leak as a result of the air loss.
Mark the area of damage with a felt-tip marker and allow the air mattress to dry completely.
Deflate the mattress fully, if it is not already completely flat.
Cut the velour fabric to fit the size of the leak.
Apply a layer of glue to the bottom of the fabric piece. The glue will be included it the patch kit.
Place the patch onto the damaged area. Press down on the patch to set the glue.
Allow the glue to dry for at least 12 hours.
Inflate the air mattress to ensure that the leak is fixed.