To relieve you of the biggest scare, no worries. Most likely, your data is save and sound in the cloud. Waiting to be uploaded.
When using an Iphone, it's good to understand that Apple has software running to make the phone as efficient as possible with the aim of minimizing battery usage and maximizing speed. This means that Apple is constantly looking at whether certain processes can be shut down. The upload process in the background is an example of this.
What can I do about this?
Luckily, you can work around this in two ways:
Keep the app open and the phone not on sleep mode.
Use the app for a longer period of time, it seems that Apple then shuts down the background process less quickly (but they don't give any information about this
What also helps is to hang it on the charger (if the workplace is set up for this). The background processes also run a bit more smoothly then.