Maybe BlackBerry can learn something from Microsoft and the Surface
I've read several articles lately about the Surface Pro 3 (here's one from the Street). It seems that the sales of the Surface Pro are finally starting to show some real growth (though they still account for only a tiny bit of the market). This seems to be because:
A) Microsoft is spending a lot of $$ on a sustained Ad campaign
B) The Surface Pro 3 is finally a bit of hardware that people want
And potentially (coming soon),
C) Windows 10 is getting some hype as an answer to the Windows 8/8.1 woes
In a lot of ways Microsoft and BlackBerry were in similar situations going into this. MS had ignored the tablet market to start with, and fell far behind iOS and Android. Then they released a product that had potential, but was so much of a departure from their legacy fare that they alienated a lot of their customers. They also released some hardware that wasn't properly spec'd (and was alpha hardware) and that didn't help. Over time, they sorted out the problems with the hardware (finally releasing the highly-rated Surface Pro 3), and are on their way to sorting out the problems with the software (with the Win 10 release).
Compare this to BB releasing the first BB10 phones with underspec'd hardware, an immature OS, and alienating their core users. Then BB goes through a few iterations before offering a more 'legacy' experience with the Classic and a high-spec experience with the Passport, and the updates to the OS (10.3.1 - yes, it still has some issues).
The thing that BB cannot really match MS on is the marketing, as they don't have the same budget. Also, MS users were pretty much tied to the OS because of the reliance of businesses on their software. However, that would have changed if MS didn't listen to their customers and backtrack from Win8, while still continuing to publicize their hardware/software.
Notice that even with the updated hardware/software MS is only making inroads into the market very slowly. If BB wants to regain some market share they're going to have to realize that they're going to have to publicize their 'hits' like the Passport, and also that it's going to have to be a sustained Ad campaign. There are no silver bullets to fixing the market share.