It sounds like you’re using the Keyring Social Importers, in addition to Keyring. I guess it’s hitting a full page of duplicates, and then bailing from checking the rest, because it doesn’t import anything in a full batch?

As a hack, you could try removing the check in keyring-importer-instagram.php around line 226:

// If we’re doing a normal import and the last request was all skipped, then we’re at “now”
if ( !$this->auto_import && self::NUM_PER_REQUEST == $skipped )
$this->finished = true;

Remove that whole block, and see what that does for you. It might leave you in an infinite loop though, so you’d need to manually bail out of the import.