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.
Exactly the same... Annoying. Tried to contact support but there seems to be an limited time of allowed support (buy to get help). I thought you should get som sort of customer support but no... Hopefully we can get help from here. I'm not a happy customer at the moment.
Just download the latest build from Parallels site manually and install it. Links in my signature if you can't find it.
