Can you confirm that you have background app refresh enabled?
Also, please try having the app uninstalled then re-installed and test to see if the issue persists.
We'll await your feedback.
A few updates to the app have occurred and the issue has been partially resolved. If I have tasks unfinished at the end of the day (i.e. 2), the next day the badge count updates automatically to include any new tasks for that day (i.e. 5). However, if I have completed all of my tasks so the badge doesn't show, the next day the badge does not appear until I go into the app and then back out.
Thanks for the follow up, our development team is still looking into this, and we're hoping on having this fixed soon.
We're sorry the inconveniences caused.