The Wave device stores the data locally on the device itself for 1 year.
The Wave Plus & Wave Mini store data locally for 80 days.
This means you can go for long periods without phone connectivity and still obtain your measurements. It will just need some time to sync.
We at Airthings recommend you connect your Wave to your phone as often as possible (at least once a week) to be able to visualize your data and make the most out of your machine.