I think it's a combination of factors:
1) Particularly challenging summer for the film industry, and challenging box office trends in general
2) Too much time between Star Trek reboot movies. The 4-year gap between Star Trek (2009) and Into Darkness (2013) was inexcusable.
3) Marketing for Beyond did not mention the 50th anniversary or really tell anything about the film, other than showing action scenes. That's not enough nowadays. Marketing has to make the film seem unique--it has to feel like an event that people should want to experience. People need a reason for why they should care--otherwise they will ignore it. In the modern world, marketing films is about cleverly getting people's attention, not just telling people the film exists.
Also, it's ironic that in the very negative times we live in, marketing failed to promote the positive message of Star Trek, ie, it's raison d'etre.
Not sure you can psychoanalyze the fan reaction to Into Darkness and tie it to this. The fan reviews of Into Darkness on Rotten Tomatoes and Amazon are quite positive. For some useless anecdotal evidence, my friends who are not big Trekkies liked the previous films but aren't rushing out to this one. I just don't think it seems urgent to them.
If they do a Star Trek IV about Kirk and his dad, they should make it a plot-heavy time travel story. Trim the budget to $150 million, or less if possible. Time travel to 2017, to save even more money. Do not focus as much on the crew. Focus mainly on Kirk. Make it personal. Have him working closely with his father, going back in time. And finally, release it Father's Day weekend 2018. Now that's marketing.