Does Consulate really care to consider sponsor's role?

[cajatt]

My father is retired and ofcourse income from pension would be low and my mom is a housewife.

1) It makes sense when interviewer asks about the income of an applicant who is retired. But its bizarre to reject the visa on low income basis even though applicant had a sponsor. What could be the basis of such a decision?
2) Is there a way to appeal to US consulate if they reject the visa because of applicant's low income? My parents had a letter which I addressed to the consulate officer but she never intended/cared to read it.
3) Has anyone else gone through this situation where their relatives' visa was rejected because the parents were retired and had only pension as their income? What was their approach next time when they applied for the visa?

Thanks,

[immihelp]

In any case, including this type of case, it is entirely their wish whether to give visa or not. Nothing you can do.