2hbh advantages;
1). Easier hitting on the rise (easier to do with added stability of 2nd hand)
2). Easier returning serves (ditto reason above)
3). Easier re-directing pace (ditto reason above)
1hbh advantages;
1). Heavier weight of shot/topspin (1hbh is a faster and freer stroke)
2). Greater crosscourt angles (due to more topspin and reach)
3). Greater lateral reach (due to reach not limited by 2nd hand)
I asked my coach if the 1hbh is dying out and he said it never will, it is just going through a phase of low popularity.
Interestingly, if the game is favoring heavier and heavier spin, the 1hbh has an advantage in at least one area over the 2hbh, as topspin is so much easier to create on the 1hbh than the 2hbh. Gasquet's backhand regularly clocks in the same rpm range as Nadal's forehand.
However, the ease of coaching of the 2hbh, combined with the fact that most pro's take up the game when they are around 5 years old (and too weak to hit a backhand with one hand), means the 2hbh will probably always be dominant in terms of popularity.