Should they train with the students if they are able to? Thoughts please. Why some don't if they are able to? 
In the past I would have just said "yes", but really there are a lot of variables to consider...
What if someone has 250 students? --is 60 years old? --teaches 5 classes a day, etc?
In general, it's probably good for instructors to train with students --at least to some degree-- but in some cases it can be a lot to ask.
I think they should get on the mats and train. I try to train with the students as much as I can. 
Yes.
When instructors don't train with a significant sample of their students, I become skeptical of their actual abilities.
Further, I think a core part of learning BJJ is "feeling" what it's like to roll with those who are more technically effective than you, which should presumably include your instructor. If they never roll with you, they're cheating you out of that
Now, that doesn't mean all instructors should be required to roll with all students every single week. As noted above, that may present some pretty significant practical issues. Also, an instructor who's rolling with everyone else is necessarily not watching the class as a whole, so he can only see/correct/comment on the indicidual students he's training with and is a little blind as to the other students.
But, the bottom line is that I do think part of the learning process is rolling with your instructor, and everybody should do it from time-to-time. I also think higher belts and instructors should be using lower belts to keep themselves reasonably sharp.
We have about 20ish students. And 4 browns teaching us personally.
Yes, but that doesn't mean that they have to roll every damn time.
That's take a toll on their body.
15 years training under him and my instructor still does, even though he's in his 40s.
Not as much as he used to in his twenties, but he still gets in there and mixes it up with the purples on up.
I'm a black belt and occasionally he makes me want to throw my belt away and quit bjj he beats me so easily.
My judo instructor too.
So yes, not with everyone all the time, but instructors should get on the mat with students.
I've only rolled with my prof 2 times....but it was enough. He's a killer
ill do some private classes with my instructor...to see how far i gotta go...its great and i thank him for it.
Even Carlinhos still gets on the mats and trains with us
My coach is 47 and kinda a freak of nature, but we roll on average 5 rounds a class, and I'm the one gasping for air after. Coaches should roll if they are physically able to. Best way to gage the progress of their students.
Does a personal trainer lift weights with everyone of his clients?
When he tells you to bench press is he doing it also? Are you paying him to run sprints beside you to get in shape with you?
I'm sure your personal trainer works out everyday you might not be there though.
56 I roll with my students ,but also listen to my body!When I train with teachers I'm tapping quick I wanna die in my gi!
I'm an instructor and I roll in most classes, although I have to have rest sessions. I tend to roll less in days classes as I usually have stuff to do straight after (pick up my boy, food shopping etc) so can't immediately shower.
Out of interest, I have heard people say there could be an issue with liability insurance if you are training yourself and someone gets injured. They could say you should have been watching and if you had been the accident prevented. Obvious counter argument is that even if you weren't training you can't watch every pair all the time... but it's worth considering.
ogkennyg - Should they train with the students if they are able to? Thoughts please. Why some don't if they are able to?Yes, and I do every time.
Yes they should train with their students, but that doesn't mean they have to train every day and every round.
IF he can, sure! Ours does.
It's its just test him don't bother. If they guy has upper belts tearing up the deep end of the mats you know he is a good teacher.
I teach a BJJ class for beginners and I roll with as many of the students as I can.
Be 48 in January and still try to roll with a fair amount of people every class. I am however, selective these days with who I pair up with. My body doesn't respond well the next day to hard rolls with the young animals anymore.
I wish my coach still did