As a Summoner I've felt like the weakness in general is in gimmicky fights. Like stand on stuff to remove Doom requires a lot of skill to actually get a pet to survive. I also found it terrible against the Malboro where you had to eat fruit, but your pet doesn't get the fruit effect (This was on SCH though, but same problem remain as SMN). I've also felt the job suffering when you need to kill popped stuff as soon as possible, because DoTs are not fast and do not do well with stuff appearing all over the place.

In short, I find the class/job fine at stuff that is focused on dealing damage over time, but suffering from "do or die" mechanics not covering pet survival.