You have identified the core issue. It is the elephant in the room.
The 2008 constitution, which was passed by a so-called referendum, which was neither free nor fair and which you cannot really call it a referendum, as it was more of a theatrical event, is a deeply flawed document. Aung San Suu Kyi recently called it “silly” and that's actually quite an apt descriptor. It essentially, through a number of different provisions, gives the military a trump card of de facto control over civilian governance, which they used for many years but have now relinquished to a supposedly civilian government. They can dismiss parliament. They can declare a state of emergency and dismiss parliament. They continue to have the right to appoint key security force personnel officials, including the Home Minister, who can in turn enforce the problematic laws that are on the books in Burma. As a result, you do have the creation of a sort of two-headed government where, yes, you can have elections—and they did—to allow a new prime minister who is not a military leader, but you still have, because of the constitution, a military that has all of these powers over civilian governance. That is the core problem that will continue to bedevil Burma for a long time.
Now the political situation is as Aung San Suu Kyi has said, that the constitution needs to change. A lot of people get hung up on the particular provision in it that disallows her from being president. It's provision 59(f) of the constitution that bars people who are foreigners and people who have spouses or relatives who are foreigners from being president, which was put there precisely to keep her from ever being the president. That's an issue that needs to be addressed, but that is not constitutional reform in and of itself.
The real constitutional reform is eliminating all of the provisions that gave the military all the powers I just noted. To do that you need 75% of the parliament plus one. Since the military holds 25% of the seats through the constitution, you have to have at least one of those 25% vote to amend the constitution. That's the de facto veto they have, the de jure veto they have, over amending the constitution. This means that any amendment that ever takes place or repeal or, God forbid, decision to have a constitutional convention that rewrites the thing from scratch, has to be a political event not a democratic one.
Since it has to be a deal of some sort, Aung San Suu Kyi has to figure that out somehow: basically a deal with the military whereby they allow the constitution to be changed.
The only other methodology for changing it would essentially be a political crisis, an uprising that forces the military to relinquish the power because they don't want the country to devolve into crisis.
There's one last way you can nudge the door open on constitutional reform, and it's a little bit complicated, and we haven't been talking about it. As you're probably aware, there is a state of armed conflict in several other states in the north and the east of the country, in Kachin, Shan, and Karen states. In the efforts to have peace agreements with the different insurgencies—and Burma has more insurgencies than pretty much any government in the world—the peace agreement that would have to be created, if there ever were to be peace with all those insurgencies, would by definition require amending the constitution, because, after all, that's what all those insurgencies want. They want the constitution to be amended so they can have more autonomy and a lot of other things. That's another avenue for amending the constitution, the diplomatic necessity that there be amendments to the constitution in order for there to be a peace deal.
However, knowing what I know and probably what a lot of you know about the peace negotiations, I wouldn't hold out any hope for that happening any time soon.