I use android, so…
Test Bambuser and Dropbox.
Dropbox will automatically upload video (or pictures) when off button is pushed or recording stopped. Just make sure the app is running in the background. Not live streaming, will only upload after recording stopped.
Bambuser is live streaming and will continue to record and upload even after off button is pushed. Unsent data is saved to phone and can be uploaded later to complete video record.
As always, test these apps under different situations and know their ins and outs.