As someone who has achieved M7 with sona I'd like to give my opinion on this.
Sona Starts off with a base mana (Without Runes) of 341 that's not a lot for someone who is Based around mana usage
Lets start with her Q then, It costs 45 Mana at lvl 1 and at max 65, that's not a lot and its a fair value and is super useful if building full AP
Now her W, this damn W, 80 Mana at lvl 1 yes just lvl 1, and it goes to a max of 100 mana, now me as an avid sona player the max amount of mana I have by the end is maybe around 2000-2300 or so maybe a bit more, and if there are a lot of team fight's ill be using this like nobody's business including when I have to use Q and E in the mix, draining me to close to half or more after a team fight or in between a team fight.
Also her E, It has a static cost of 65 which isn't to bad late game but hurts early game and it has a pretty good price nothing to say on this.
And her R cost's 100 mana each time you use it.
Now lets put this together shall we?
in the end you spend about 330 mana using every single ability at Lvl 18, but now most games don't last till you get to lvl 18 so typically you might max Q, but still be missing a point or two on her W and barely anything on her E
So lets take it you max Q, and are missing two points in her W and 3 in her E and have ult.
You use about 320 mana, only 10 less or so then if you were lvl 18
Now with team fights once that W is off cool down you'll probably use it again draining you of 90 mana each time.
This take's a lot and unless sona has a blue buff thrown on her she looses mana and has to re-call quite often, leaving her alone in lane and let her just move around lets her regen her mana and she regen's it relatively quickly.
But even to that in lane alone she might loose over half her mana trying to save her ADC and on top of using her ult wasting around 200 or so mana when you only maybe have 700-860 or so mana is A lot for a sona player.
Thanks for reading, best of luck to you.
~Frost