First, from the description its not clear how the videos are being stored when they are being taken while flying.
Are they recorded to the internal drone memory?
Are they recorded to the removable micro SD card?
If recording to the internal drone memory not sure what the drone does when it gets full of videos? Someone will know here but can only think of two possible options;
1) stop recording (videos lost past device full) My guess is this one
2) delete older videos and replace with newest videos? My guess is NOT this one
Are you flying with a Micro SD card?
If so, what size and type of Micro SD card are you flying with?
If so, how are you confirming which device its going to record to?
Getting any data off the internal drone memory requires the drone to be power up (not necessarily to the controller either) but burning a battery that has to be recharged later.
I use the Micro SD all the time. Drone off, and or drone battery not installed and just remove the Micro SD card and place it in my adapter for the computer.
Have not lost any data (videos or pictures). Only if I inadvertently turn off recording while flying.
All videos and pictures placed on computer. Not sure 4K will even help make any better picture on a phone. Sure looks good on a big screen TV though.