***** A NON-TEACHER's COMMENT *****
(1) A great question!!!
(2) I may have found the answer in Professor Paul Roberts's
Understanding Grammar (1954).
(3) That scholar explains that some words may be a fragment in
one context and not a fragment in another context.
(a) "While we were waiting." Is that a fragment? Professor Roberts
says that it is not IF you say it in answer to the question: "When did
you see him?" On the other hand, it is a fragment if you write it this
way: We discussed that and several other matters. While we were
(4) Maybe (maybe!!!) your example is not a fragment IF it is an answer
to the question: "Why do you look so sleepy?" On the other hand, I
guess it would be a fragment if written: Because my children were sick.
I was up all night.
(5) To be on the safe side, it would probably be better to rewrite your
sentence something like:
Because my children were sick, I was up all night. / I was up all night
because my children were sick.
Student or Learner