She could be afraid that if she starts crying over something that's affecting her deeply, she may not be able to stop. Sometimes crying also has unpleasant side effects like headache or muscle aches in the face and shoulders, and a stomach ache.
Rather than trying to assure her that it's okay to cry, sit with her and inquire into what she's afraid of. She may need some quiet, calm coaxing if she's fighting off tears, or it might be even more helpful to have this conversation while she's not near tears. Ask her what she envisions will happen to her if she cries. This may give her the permission and support to explore her worries in more depth. That will probably need to happen before she can move past this phase.
There are many fabulous tips like this on how to help your children deal with their own emotional quandaries in the wise book How to Talk So Kids Will Listen, and Listen So Kids Will Talk, by Faber and Mazlish.