Health issues in grad school - how many extensions are acceptable? I'm a graduate student in physics, and I've been having some major health issues.  For the sake of anonymity, I don't want to say what they are, but they are NOT mental-health related, though they certainly have caused quite a bit of depression as a byproduct.  I make this distinction not due to some prejudice, but simply because mental health problems come with their own specific challenges that are not always shared by other illnesses.  I chose to mention physics with the hope that someone with knowledge of the physics-specific culture could comment. Also, I think it's worth mentioning that physics seems to have a particularly brutal academic culture (though I haven't experienced that in my program...yet).  I'm currently struggling to complete my assignments on time, and it's very frustrating.  I've done well in all of my courses so far, but now I'm falling behind.  

There is one class in which I'm particularly behind, and I asked the professor for a two day extension on a problem set.  That day came and went, and I still was not able to complete the assignment.  I would need another two days most likely, and if I can't complete it then I will have to drop the course.  I would like to ask for another extension, but I don't want to appear flaky or unreliable, and I'm concerned about gaining a reputation in the department since I've asked other professors for extensions in the past (which have been granted and I was able to get the work done). If I had an advisor already, I would be more willing to just ask for the extension, but since I don't have one yet, I'm very self-conscious of being perceived as one of the "good" students.  This class is not required for my program, but could establish me as a more capable student by going beyond the basic intro courses.  Other students my year are taking similar "above and beyond courses", so it seems to be a way of proving yourself to a potential advisor.  Plus, I just really don't want to drop the course, since it's interesting and I don't want to let it "beat me", silly as that sounds.     

Is it acceptable to ask for another extension?  I've done well on all the other assignments, and I could explain what's been happening.  However, I'm also concerned that explaining my situation could backfire if having an illness could make potential advisors more wary of taking me as a student.
I would have some general conversation with the department, and with health services versus these atomistic requests for extra time on specific projects.  
If the situation is chronic, perhaps you need to defer your studies as you are routinely unable to keep up.  But that depends on the specifics: frequency and duration of your issues, are they predictable (e.g. chemo timing) or random.  Likelihood to improve.  And of course if the situation is a genuine medical impairment or if you are struggling with content and using it as an excuse (not an accusation, just within the theoretical solution space).


P.s.  If the course is not part of the requirements, I would just drop it.  Seems like obvious way to handle the impairment.  You can still get your program done.  Just not with extra volume.