In the room with the 3 fireball-spitters on the left, which you have to bounce into the machine on the right, the spitters randomly stop shooting the fireballs, making it impossible to finish the puzzle.

I tried to go around this by completing the 2nd/3rd first, but it still stops randomly.

Are you sure they top at random?
Once you light a furnace, the spitter that's aligned with that furnace stops working. So if you only lit 2, only 1 spitter should be working.

If indeed, all 3 of them stop working and you still have 1 or more furnace off, then your save file is bugged.
You can try restoring an old save file.
If you don't have one, you can use mine:
http://www.mediafire.com/download/v5jpgniqxxtq734/sg.zip
The file location in Windows is: C:\Users\<your username>\AppData\Local\The Way\

But be warned, the other 2 generators are already cleared so if you still had another one to do, you will miss out on it (but if you are stuck, then there's no other way around it)

Sadly, it is like I described, so it appears my savefile is bugged, but I already cleared the other 2 generators, so your savefile is a gamesaver for me.

Thank you very much.

Glad I could help.
From now on, keep making backups of savefiles at regular intervals in case the game bugs again.
I make backups of savefiles for every game I play. You never know when you (or someone else) might need it.
Sadly, with the way the games are coded and tested nowadays, backing up save files has become mandatory.

Thing is, I had a backup of sorts, since I played the game on both my desktop and laptop, and simply copied the savefile from one to the other.

Sadly, the bug appeared on both systems.