It is the opponents battle phase. The cards on the field (and elsewhere, for reference to if necessary) are listed below. "Lightspulsar Dragon" was summoned this turn, in the main phase, by banishing "black dragon collapserpent" and "
"raiden, lightsworn assailant" from the graveyard, while the opponent had no other cards on the field or hand and I had the cards described below. "Lightpulsar Dragon" had declared an attack on "level eater", I had activated the third effect of "shooting star dragon", banishing SSD and negating lightpulsar dragon's attack. No other cards or effects were activated in this turn. During the end phase, Shooting Star Dragon was not special summoned by its own effect but remained banished.

This seems to constitute an error as far as I can see, as no cards or effects I can see or that I saw played were used that could prevent the special summon of shooting quasar dragon, however I would like confirmation of this. Also I would like to know if anyone else has experienced a similar problem with this card.

Cards on the field:

Opponent: Lightpulsar Dragon

Myself: Shooting Star Dragon (special summoned in a previous turn by the effect of "shooting quasar dragon", Level Eater

Cards in Graveyard:

Opponent:galaxy cyclone, solar recharge, card trooper (x2), charge of the light brigade, darkflare dragon (x2), BLS-envoy of the beginning, lumina, lightsworn summoner, chaos sorcerer (x2), white dragon wyverburster, black dragon collapserpent, raiden, lightsworn assailant

Myself:swift scarecrow, one for one, junk synchron (x2), tuningware (x2), samsara, dragon of rebirth, scrap-iron scarecrow, cyber larva, tuning, great old one hastur (in the newly released English translation of the card, but not on the current game version, this is known as "old entity hastorr"), reinforcement of the army, doppelwarrior, drill synchron, synchron explorer, junk warrior, phonon pulse dragon, quickdraw synchron, level eater

Cards Banished:

Opponent: raiden, lightsworn assailant, black dragon collapserpent, galaxy cyclone, gorz the emmissary of darkness, white dragon wyverburster, lightpulsar dragon, lyla, lightsworn sorceress, battle fader (x2), breakthrough skill

Myself: jet synchron (x2), jet warrior, shooting quasar dragon

Cards in hand:

Opponent: none

Myself: tuningware

TL;DR: shooting star dragon used its effect to banish itself to negate an attack from opponent's lightpulsar dragon on my level eater, but was not special summoned by its own effect during the end phase. No other cards were played that turn. Is this a error, or is there some reason why SSD should not summon? Has this happened to anyone else?
There is indeed a reason that Shooting Star Dragon did not Special Summon itself during the End Phase. When Shooting Quasar Dragon's effect Special Summons Shooting Star Dragon, it is not a proper Synchro Summon. Because of this, that Shooting Star Dragon cannot be Special Summoned from the Graveyard or banished area. The same thing happens in the case of, for example, Fusion Monsters that are Special Summoned by the effect of Summoner of Illusions -- they were not Fusion Summoned properly, so they cannot be Special Summoned from the Graveyard or banished area. (By contrast, a Fusion monster that is Special Summoned with Instant Fusion can be Special Summoned from the Graveyard or banished area, unless its own effect says otherwise, because even though it doesn't use any Fusion Materials, the Special Summon that Instant Fusion performs is treated as a Fusion Summon.)
Yep, because SSD was summoned by Shooting Quasar, it is not counted as being summoned properly. So when SSD goes to the grave, he cannot come back.