This is a nice writeup, so don't consider this post a criticism of yours, but rather just an attempt to add unto it.
I don't believe the reason for Fire Emblem 6 heading to handhelds was made because handhelds started outselling consoles in Japan, but rather because they got into a tricky copyright situation.
The creator of Fire Emblem, named Kaga, was the main man behind all the first five Fire Emblem games. Just after releasing Thracia 776, he left Nintendo over some disagreements, and started a new team. With the new team, he attempted to make a game called Emblem Saga for the original Playstation, even using assets from Thracia 776. He'd brought with him the man behind the art of Thracia 776, so they were now trying to make a game using the gameplay that they had created, with art assets that they had created. But, the Fire Emblem franchise belonged to Nintendo, and so did the art assets, so Nintendo threatened to sue them over copyright infringements.
In the end, the game was released as TearRing Saga, with gameplay similar to Fire Emblem, and art similar to Fire Emblem. In fact, any logical console follow up of Fire Emblem on the N64 would have to be very close to what TearRing Saga was.
This would be problematic, because if a Fire Emblem 6 on the N64 ended up being inferior to the TearRing Saga games - which it quite likely would have had - that would likely be an end for the series.
So instead, Nintendo opted for releasing a bare-bones Fire Emblem 3 gameplay style game on the GBA. It had virtually no new concepts, and had removed nearly all the new, interesting concepts from FE4 and FE5. Removing old concepts wasn't anything new for Fire Emblem - all the first 5 games had been radically different from each other (with somewhat of an exception with FE3 being a simple of FE1 in both story, gameplay and style).
Anyway, Fire Emblem 6 was reduced to little but the core Fire Emblem concepts, which was a necessity to differentiate it from TearRing Saga, which had released very successfully (outselling Thracia 776 by a decent margin) just the year before.
As for the falling sales figures of Fire Emblem since FE7, I think it's largely due to a lack of experimentation.
The first five Fire Emblem games were, as previously mentioned, wildly different from each other. Thracia 776, while a sequel to Genealogy of the Holy War, plays entirely differently, and the strategies required to win are of a completely different nature. The same was true from FE3 to FE4, and from FE2 to FE3.
But Fire Emblem 6, 7 and 8 could virtually have been the same game. The story in each is different (but eerily similar), and there are minor tweaks (such as the non-story missions of FE8, and its world map), but there are no new mechanics added, and the strategy required to win each is the same.
With Path of Radiance, they made some changes, but largely kept things the same. It readded the skills from FE4 and FE5, introduced a new take on the manaketes - the Laguz, and improved the base settings. These were, however, minor improvements to the old concepts. It also featured what is probably the ultimate rendition of the classic Fire Emblem story. It also added shove, which was the first new mechanic added since Kaga left. Path of Radiance attempted to change things, although quite slightly.
Radiant Dawn then continued Path of Radiance's trend of building upon the previous game and then adding small elements (which is really something the series never did in its first 8 games), by adding third tiers, skills beyond what the series had ever seen and split groups of teams, as well as taking the story to its extreme.
The problem following Radiant Dawn, I think, was largely where to go from there. Going back to the classic Fire Emblem style plot (ala 1, 3, 6, 7, 8 and 9) and game layout would be difficult, because there was no clear way to improve on Path of Radiance's rendition. On the other hand, topping Radiant Dawn's scale and intensity would be impossible without a tie-in. They couldn't do what they'd done from FE8 to FE9 and FE9 to FE10 again.
So instead, they went with making two remakes, with little success. They went back to the problem of FE6, 7 and 8, where each game plays exactly like the last.
But then, with Awakening, Intelligent Systems went back to the style they had under Kaga. They abandoned the great ideas of Path of Radiance and Radiant Dawn (just as Mystery did with Gaiden, Genealogy did with Mystery, and Thracia did with Genealogy), and introduced completely new gameplay and story mechanics. The strategies required in this game were different from what they'd ever been before.
And it was a massive success.
But what's much more promising for Fire Emblem's future than that one-off success, is that Intelligent Systems has learned an important lesson. Each iteration of Fire Emblem needs to be different from its last. And its mechanics and chapter win-requirements can't be too complex (a problem both Thracia 776 and Radiant Dawn - the two titles with the least commercial success - had).
Because FE14 (or Fire Emblem If, if you will) looks to both have different mechanics than Awakening, have a different plot, and have different chapter layouts. Whether it goes the FE2-5 style of completely ditching what made Awakening great, or the FE9 and 10 route of improving on it, remains to be seen, but either should result in a great game. Certainly a better one than they would by doing what they did during the GBA era, which would have been just making Awakening 2.0.
One final point; I think the rumours of Fire Emblem nearly being cancelled have been very overstated after Awakening was released. The quote from the Intelligent Systems person states that Fire Emblem might cancelled if the next FE sold less than 250,000. The chances of FE13 selling less than 250,000 were always extremely slim. Keep in mind that that would mean selling less than half of what Radiant Dawn did. Or in other words, less Worldwide than any internationally released FE has done in the US alone. This, at a point in time when Super Smash. Bros series had ensured that the Fire Emblem series was known by more people internationally than ever before.
The game would have had to been complete and utter rubbish for that to happen. And even if it were rubbish, I'm not sure it would have sold less than 250,000.