By what I know, in the "Journal of Two Sisters" (Luna and Celestia diary) is mentioned they rejuvenate themselves by moving the sun and the moon, therefore living for thousands of years.However if that was the case, Celestia would appear to be much more younger than Luna, since the her sister was trapped in the moon while Celestia was rejuvenating herself for the lat 1000 years. Also both princess would look younger as time goes, since that is what rejuvenation means, but the flashbacks made it clear that also doesn't happened in the show..So by what happened, there not much room for doubt, alicorns must be immortals or we would have a inconsistency in the story.Probably the implications of alicorns being immortals would be something not belonging in a kids show, as the very idea of Cadence outliving her husband and Twilight outliving her family and friends (what also imply Celestia cursed Twilight when promoting to princess) would be very grim. I think they prefer inconsistency.Unless Meghan meant Twilight was going to die, what I think is very unlikely.One could argue Twilight and Cadence were fake-alicorns therefore not being immortals, but this doesn't apply to Flurry what bring the whole question again, so I guess they prefer to play safe instead of going for a consistent story.Well, anyway you could still claim headcannon