Each round of combat follows the following steps:
I: Space Combat (one round)
II: Ground Combat (one round)
III: Retreat Step
IV: Next Round
Death Star Plans can be played between steps I and II of each round of the combat if the conditions are met (there is a Rebel Fighter and a Death Star present) and you haven't played any other Objective cards in that Combat.
So yes, it can usually be played once per round between the Space and Ground battles of those rounds.
Note also that it is merely "revealed" at this point unless you actually succeed, in which case you "play" it. This is important when you consider the limitation on playing only one Objective per combat - an unsuccessful strike on the Death Star does not count as playing the card.