1) Is the extension enabled in the default configuration scope?
Check if it is enabled. It will be in Admin -> System -> Configuration -> Review Email -> Enabled. If you are running multiple websites within one installation and only want to use the extension in one, always enable the extension in the default configuration scope and overwrite this in the other stores by setting "Enabled" to "No" on the store level. A cron always runs in the global scope.
2) Is the “use cron” option set to "Yes"?
Check if this option is set to "Yes" in the default configuration scope. It will be in Admin -> System -> Configuration -> Review Email.
3) Do you have reviews in the schedule?
Check if there are review emails that are already overdue.
It will be in Admin -> Newsletter -> Review Email -> Scheduled emails. There should be some emails with the status “Scheduled” which must be scheduled for a later date.
4) Is the Magento cron running?
Magento depends heavily on its cron. As of Magento EE 1.14.1 and Magento CE 1.9.1 all Magento e-mails (including order confirmation and transactional) are sent by cron.
It's also used for tasks as: DB log cleanups, sending newsletters, generating Google Sitemaps, etc. However, many people forget to set up this cron.
You can check if the cron is running by checking the the cronjob timeline using the AOE Scheduler extensions. With this extension you can manage, view and test your scheduler/cron tasks including a timeline. You can download this extension right here.
With the AOE scheduler extension it's possible to get a timeline view of all the available cronjob tasks. It scans the xml configuration from Magento and your additional extension (including our extension) and generates a list of all tasks, while also considering those tasks, whose intervals can be configured dynamically within the Magento backend (e.g. sitemap generation). You can also choose to run the task directly. Be careful with that, as the execution might last longer than a few seconds or might depend on some other command line environment settings. For testing small tasks this might still be a safer option.
After installation, navigate in the admin to Systeem > Scheduler > List View. Sort this tabel on Status > Success to check if there are jobs that have run successfully. Also in this screen you will see a notice of the heartbeat of the cron is running.
If there are no successful runs, this means that you have not setup the Magento cron. Please ask you hosting provider to fix this.
You can find this information under System > Scheduler > Instructions.
Please note that setting up a Magento cron is part of the Magento installation & configuration.