Apple iOS system includes an automatic iCloud backup feature, utilizing the free 5 GB iCloud storage included with your Apple ID. This page has details on setting it up: iCloud Backup.
When the iCloud backup is turned on, then all app data including your LogTen Pro logbook will be backed up to iCloud whenever your device is plugged in, connected to WiFi, and asleep -- usually when you are!
All apps are included in this backup by default, but it is possible to exclude apps from it to save space. The downside of this backup is that it is not possible to restore data for individual apps (meaning you have to restore your whole device from an iCloud backup), but it is very useful if it becomes necessary to transfer to a new device for any reason.