It's very tedious to export one by one when you have tens to hundreds of log files and you want to export all of them. A mass export option would be helpful.
So... turn off "stop on error/stop on warning" and create your automation to only stop when you want it to. Then, wrap your execution in try/catch/finally logic so that, when you DO run into an exception that causes you to have to halt the tests, you still export the log.
OR... you could implement "OnStopTest" event handler so that, when the test halts, you will execute log export.