'Update WordPress Database' keeps on appearing

At my workplace we have multiple users of WordPress, and all keep on getting the ‘Database update required …’ followed by ‘Update wordpress database’ button. We click, it gets updated, life is good, but then it appears again after a while. If we don’t click, we get lots of 404 errors on the site. I don’t understand why we would be asked to update DB when the last version update of WordPress was 3.3.1 in January …

Would anyone know why this is happening and how to stop it from happening again?

Thanks ??