Perhaps the bird’s magic is limiting its summon level?
Well… I just had a funny little interaction while testing this. Took my level 5 untraited Sunbird into battle with 15 magic and casted it. It respawned as a level 15 sunbird with higher stats, as I expected. After battle, it was still level 15, now with 20 magic. If done more than once, I could get him up to his current level cap. Playing another battle or restarting the game reverts him to level 5, so its an issue with client data storage (like the 9x stat summons on Warlord IV).
So yes, the bird’s magic affect its rebirth level. This would make him a rather bad troop early game, where you don’t have the skill bonuses would continually summon it at a lower and lower level, much lower after the first cast and probably one-shottable without significant magic bonuses (base magic of 7 at level 17, which would utterly cripple it after one cast). In contrast, Werewolf and Villager will be at their current level in your collection (but this is a transform, not a summon) and do not suffer this problem, but you have to obtain and develop them both for them to be effective.