The writers explained during the Q&A that R2-D2 is in this sleep mode because he's grieving in his own way, just like Luke Skywalker is by hiding himself from the galaxy. And as for the map info, which includes locations on ancient Jedi temples that Luke may be after, Arndt says that's a call-back to Episode IV, the film that started it all.
"We had the idea about R2 plugging into the information base of the Death Star, and that’s how he was able to get the full map and find where the Jedi temples are."
In the original Star Wars movie, Luke, Han Solo, Chewbacca, Obi-Wan Kenobi, C-3PO, and R2-D2 are aboard the Millennium Falcon leaving Tatooine and heading towards Alderaan but are captured by the Death Star's tractor beam. And while on this station, they take the opportunity to mount a rescue for Princess Leia who's being held prisoner and during this sequence R2-D2 plugs into the Death Star's computer systems, gaining access to the Empire's databases. Abrams says they didn't spell this out in Episode VII because he didn't want to spend time detailing events from decades earlier but basically, R2 got the map info there.
This does not however, explain why this info wasn't shared by R2 previously if it includes unexplored systems the Republic and Resistance are unaware of or why there's a missing piece that shows up on Jakku. As Abrams also pointed out during the Q&A, Kylo Ren does mention that the First Order has the rest of the map from the Imperial archives as well.
But who made the map to Luke and sent this missing piece to Leia via Lor San Tekka (Max von Sydow's character)? Was this all Luke's doing?
As for the timely awakening of the classic droid, Abrams says:
“BB-8 comes up and says something to him, which is basically, ‘I’ve got this piece of a map, do you happen to have the rest?’. The idea was, R2 who has been all over the galaxy, is still in his coma, but he hears this. And it triggers something that would ultimately wake him up... While it may seem, you know, completely lucky and an easy way out, at that point in the movie, when you’ve lost a person, desperately, and somebody you hopefully care about is unconscious, you want someone to return.”
There you have it. The reason R2-D2 wakes up is because BB-8 asked a question, one that R2 took a long time to respond to, but does so just at the right time. The logic behind these happenings though, from R2 not doing anything on his own to find Luke to no one just turning R2 on, are all lost in favor of the emotional impact of this character coming in just at the right time. It's not the perfect answer we suspect fans are looking for but now at least we understand the reasoning behind what the writers of Star Wars 7 did with the character.
And that being said, R2 is no stranger to random plot-dependent conveniences. In the prequels, the astromech droid suddenly had the ability to fly... something he inexplicably cannot do later in the saga.
It's always possible more will be revealed in the followup movies. R2-D2 does "awaken" after all when Rey and Leia meet during Rey's first arrival at the Resistance base. Fan theories on this range from R2 bring programmed to activate upon Rey's arrival (even though Rey and R2 don't see each other before this) to Luke feeling the loss of Han Solo like Leia did, but also feeling the moment Rey and Leia meet each other which sees Luke activate R2 remotely. These are far-fetched based on what was shown so far, but arguably as far-fetched as the actual explanations.
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The film is directed by J.J. Abrams and stars Harrison Ford, Mark Hamill, Carrie Fisher, Adam Driver, Daisy Ridley, John Boyega, Oscar Isaac, Lupita Nyong’o, Andy Serkis, Domhnall Gleeson, Anthony Daniels, Peter Mayhew and Max Von Sydow. Kathleen Kennedy, J.J. Abrams and Bryan Burk are producing with Tommy Harper and Jason McGatlin serving as executive producers. The screenplay is by Lawrence Kasdan & J.J. Abrams and Michael Arndt.
Star Wars: Episode VII – The Force Awakens is now in theaters, followed by Rogue One: A Star Wars Story on December 16th, 2016, Star Wars: Episode VIII on May 26th, 2017, and the Han Solo Star Wars Anthology film on May 25th, 2018. Star Wars: Episode IX is expected to reach theaters in 2019, followed by the third Star Wars Anthology film in 2020.