1. There is no HV spikes on input
2. Excuse me for my ignorance, but what is DAP? If you mean power pad under package, TSOT-6 doesn't have any.
During my experiments I've killed like a dozen of LMR's, and only one schematic solution that working stable under any possible conditions is adding a soft start circuit (drawing attached).
Didn't try just adding input capacitor - I'm little bit out of ic, so I can't risk to kill so more for now. And I'm affraid that is not the solution.
Still want to know about short-circuit protection. In the first case (without soft-start circuit) shorting the output before start or during work breaks down LMR14206.
With soft start circuit there is no such problem...