The Report subscriptions are created as jobs for the SQL Agent. You should see a long list of jobs with GUIDs as the names. Make sure that the SQL agent jobs are running. Going through the Steps of the SQL Reporting Services Configuration tool will recreate these jobs if you were to move the Reporting Service installation to another server. (I don't recall which step recreates the subscriptions. Just go through each pane and click "Apply.")
Depending on how you move things, you may need to backup and restore encryption keys, and you can easily end up in a state where two copies of subscription exist and are executed ( on different servers.) But in your case, where you didn't move SSRS, I'd look at the SQL Agent properties on the original server (Express) to see that the SQL agent is enabled and running, and check the history of the SQL Agent jobs, to see if there are any problems.