Retaining Rings hold the bottom of your flag to the flagpole on an internal design. Without this retaining ring your flag would not present correctly.
Retaining rings should be checked on an on-going basis for wear. They take the brunt of the wind when your flag is flying. They do have a wire core, however, with continuous stress the cable can become weakened. Replacing a retaining ring before it breaks is your most ecconomical solution. This is also a good time to check your halyard and snaps.