I think I can answer some questions people are having with this cards text. So I properly Synchro summoned Blade Master with the properly Synchro summoned Gladiator and Star Guardian as materials. However, I used BB’s effect to banish itself to avoid my opponent’s targeted destruction during their turn, to which it Special summons its self back to the field during my next main phase. At the moment, this card is not longer considered properly Synchro summoned thus not being able to summon its initial materials with Dragonfly’s effect.
Blade Blaster that was banished by its own effect and returned to the field is still count as properly summoned, only that it is no longer tied to the 2 materials used for it's synchro summoning.
Blade Blaster can return to the field because it WAS properly summoned, however, it no longer remember the materials used to summon it, since the last thing to happen to it was a special summon, not a synchro summon.
Konami invented some bs about cards having memory, this one doesn't have one, so then they printed similar cards, say they have memory and sell it to you for even more money
Ruling isn’t clear on this issue. For whatever reason, Blade Blaster’s materials aren’t recognized if it laves the field and then returns. This the game will not special summon them with Dragonfly’s effect.
It's not a specifically written ruling on a specific section on the rulebook, but based on rulings on other cards, it has always been like that even back when the Extra Deck is still called as Fusion Deck.
Any materials are forgotten if the monster left the field and then return to the field.
Heck, even the materials themselves forgot they are used as material, if they were removed from the place they end up in when they are used as material.
Look at the ruling for this very old card called Supply. Supply allows you to retrieve Fusion Materials you used from your Graveyard, but its ruling says you cannot do so if the materials are banished and then returned to the Graveyard.
It’s a little bit different situation for fusion monsters as it’s materials are clearly listed on the Fusion monster. However that’s obviously not the case for Synchro/Xyz monsters. But ultimately the rules are that when a monster is banished and returns to the field/graveyard, the materials are null and void.