How should a girl deal with her family's rejection of suitable suitors without clear reasons, and with their hesitation to approve a suitable suitor due to their concern about the presence of mental illness among his maternal aunts?

Our advice to you is to be open with your family and discuss the matter with them gently and politely. Inform them that you have learned about the prospective suitor and that you consider him righteous, and that his aunts' illness is not a valid reason to reject him. You can also seek the mediation of some wise relatives or others who hold influence with your family, so they may speak to them about this matter and convince them to agree. We also advise you to seek Allah's help, rely on Him, and supplicate to Him frequently.