The fabric in the photo above is fraying along the cut circle. The grommet needs a sturdy fabric to hold on to, so if the fabric is fraying (unraveling), the grommet doesn't have anything to securely attach itself to and will pull out.
(Imagine you're falling from the sky and you manage to grab onto the edge of a giant piece of cloth to break your fall. If the edge of that cloth starts to fray, you no longer have a secure hold and will continue to fall.)
A few suggestions to try: