I loved your question, I couldn't answer it, I asked my friends and we couldn't find an explanation quickly!
After one day of inner talk with ourselves, we agreed that:
We use "fue" when something was, it was definitely and it simply was, while we use "era" when something was, but leaving the possibility open for a change of it in the conversation.
"About her, the problem was we didn't see each other"
"Respecto a ella, el problema fue que no nos veíamos". This would imply that the problem was that, and nothing could be done about it. (They probably broke up because of it).
"Respecto a ella, el problema era que no nos veíamos". This would imply that probably the problem stopped existing or even was solved. (They are probably still together and overcome the problem).
"My question was if there will be classes tomorrow"
"Mi pregunta fue si habrá clases mañana". This would imply that the question was that, you are not interested on solving it, and you will probably not say what the outcome of the question was after you said the sentence.
"Mi pregunta era si habrá clases mañana". This would imply that you still have the doubt, and you are actually requesting an answer implicitly if silence comes after it.
"My doubt was regarding math"
"Mi duda fue respecto a matemáticas". This would express that the doubt just was that, you are not interested on solving it, and probably after you said the sentence you will not say whether you solved your doubt or not.
"Mi duda era respecto a matemáticas". This would imply that probably the problem stopped existing or even was solved, probably an explanation of how it disappear would follow that sentence.
Hope I was able to communicate the point. Cheers!