Yes a mite infestation could have killed her, and broodies are especially susceptible to mite infestations. Did you see mites on her? If so, then check her chicks for mites asap.
I'm really sorry about your broody hen. In addition to possible reasons for her death already mentioned, how hot has it been where you are? A broody can become severely dehydrated during extreme summer heat, since she usually only leaves her eggs once each day to eat and drink.