Have you setup the cron job in your cpanel or plesk? The cron job is found in WHMCS under Setup > Automation Settings... the two symptoms you are describing indicate to me that there is an issue with the cron job being run somehow. Do you have any errors in your activity log relating to the cron task?
Also, is this a clean install of WHMCS, or have you added addon modules and other extensions? Sometimes if those addons aren't setup and are relying on a cron task it may fail.
If you have the cron job setup, see if you can change the time to go every 5 minutes or so and see if you can get more debug information. That's probably where I would start if it were mine.