Seriously, I can't believe it doesn't auto re-summon after you die. Games like WoW implemented this for hunter pets years ago.
It doesn't add any strategic element to the game. It's effectively like an aura/stance. Imagine if all your stances just turned off when you die and you had to click them all again to activate, then think about doing that mid-fight. The only thing it does is lock out all your Falconry abilities till you remember your owl didn't rez with you.