Yes, a family-based green card application can be rejected for several reasons. While family sponsorship is a strong pathway to permanent residency, applicants must meet all legal and procedural requirements. 

Here are some common reasons for rejection:

1. Ineligibility of the Petitioner or Beneficiary

• The petitioner (U.S. citizen or permanent resident) must have the proper relationship with the beneficiary. If the claimed relationship is invalid or unrecognized by U.S. immigration law, the application may be denied.
• The beneficiary must also meet eligibility criteria, such as lawful entry into the U.S. or admissibility requirements.

2. Incomplete or Incorrect Application

• Any errors, missing information, or incorrect details on Form I-130 (Petition for Alien Relative) or Form I-485 (Application to Register Permanent Residence or Adjust Status) can lead to rejection.
• Failing to submit required supporting documents (such as proof of relationship, financial sponsorship, or birth certificates) may also cause delays or denial.

3. Insufficient Financial Support

• The petitioner must prove financial ability to support the beneficiary through Form I-864 (Affidavit of Support). If the petitioner does not meet the income requirements or lacks a qualifying joint sponsor, the application may be rejected.

4. Criminal History or Immigration Violations

• If the beneficiary has a criminal record, prior deportations, or immigration fraud (such as marriage fraud), they may be deemed inadmissible.
• Some waivers may be available, but approval is not guaranteed.

5. Health-Related Issues

• Certain medical conditions, such as infectious diseases or failure to provide required vaccinations, can lead to inadmissibility.
• The applicant may need to complete a medical examination by an approved doctor.

6. Public Charge Concerns

• If USCIS determines the applicant is likely to become a public charge (dependent on government assistance), the green card can be denied.

7. Failure to Attend Biometrics or Interview

• USCIS requires applicants to complete biometric screenings and attend an in-person interview. Missing these appointments without rescheduling can result in denial.

8. National Security or Fraud Concerns

• If USCIS suspects fraud in the application, such as a sham marriage for immigration benefits, it will conduct further investigations and may deny the green card.
• Background checks may also flag individuals as security risks, leading to rejection.

How to Avoid Rejection?

• Double-check all forms for accuracy and completeness.
• Submit all required documents and evidence.
• Ensure financial eligibility through an affidavit of support.
• Be honest and transparent during the process.
• Consult an immigration attorney if you have past violations or complications.

While rejection does not always mean a permanent denial, addressing the issue properly and reapplying with corrections can improve the chances of approval.