The maps data itself is never backed up because it can be quiet large (Apple doesn’t allow it). Normally it will remember which maps you had downloaded (as you say) and start downloading again on its own.
Perhaps check the Network Mode setting that it is set to either Online or WiFi Only. If that doesn’t help, deleting the maps from the Offline Maps list, and then going to Get Maps to select them again for download.
Lastly, if all else fails, you can use the Export/Import function to export a backup (Settings > Export > Pocket Earth Archive > All Data). Email it to yourself or use iTunes to transfer it to a safe place, then delete and reinstall the app, download desired maps, and import the backup to get your favorites back.
Note, you can use this export/import method also as a way to manually sync Pocket Earth across several devices.