I believe I'm seeing the same issue.
Parallels Desktop Update offers an update to 9.0.24229.991745 from 9.0.24172.951362 on my up-to-date Mavericks MBP
I click "Install Update." The dialog goes away. it looks like something is restarting, because I get the black "Parallels Desktop" lozenge with a spinner. Then THAT goes away too. Nothing else happens. On restarting Parallels the Parallels Desktop Update dialog comes back and the cycle repeats.
Same result if I click "Remind Me Later" then manually check for updates.