Are you forcing this app to close as described below?
If you are forcing the app to close, the app will not be able to auto sync at all as it won't be eligible to run in the background. To fix it, simply launch the app again.
It is the general consensus that forcing apps to close does not improve battery life as discussed in this articles:
Although you can control the minimum time between auto syncs using the "Minimum Interval" setting, the actual time between auto syncs is determined by iOS and is typically 30-60 minutes but it may take longer depending on a number of factors including whether you're connected to Wi-Fi, whether your phone is plugged in, how fully charged the battery is, and how often you use this app.