When an alien requests an SSN or replacement SSN card, SSA will verify his or her documents and current status with the appropriate Bureau of the Department of Homeland Security. If verification is not available through the Systematic Alien Verification for Entitlements (SAVE) system, SSA will send Form G-845 for manual verification.
RM 00203.720 Verifying Immigration Documents:
http://policy.ssa.gov/poms.nsf/lnx/0100203720 When the SSA office does send the G-845, suggest that you go back to the SSA office no more that once week with your documents to (1) ask them to check SAVE again (2) ask if they sent a G-845 (3) if yes, did it come back (4) after 30 days ask if they have followed up on the G-845 by calling or sending another mark “second request.”
http://policy.ssa.gov/poms.nsf/lnx/0100203735RM 00203.735 Requesting Online (Primary) Verification By SAVE
You can try calling the SSA Regional Office if you have waited at least 30 days and your local SSA office doesn't seem to be concerned about following up on the G-845
http://www.ssa.gov/otherssasites/Refer them to:
http://policy.ssa.gov/poms.nsf/lnx/0100203740RM 00203.740 Requesting Additional (Manual) Verification By DHS
Step 6
DHS should respond to SSA within 15 federal work days after receiving the Form G-845. If DHS does not respond within 15 federal work days from the receipt of the G-845 from SSA, follow-up with the DHS, USCIS Immigration Status office. (Allow 15 days plus five additional federal work days of mail time for the G-845 to be received at and returned from DHS. Follow local practice to follow-up with DHS.
Some SSA offices have an arrangement with the DHS, USCIS office to telephone for the follow-up contact; other SSA offices send a copy of the original G-845 annotated “second request.”) If the DHS response is still not received within 15 federal work days after the follow-up contact (if the follow-up is by mail allow five additional federal work days of mail time for the G-845 to be received at and returned from DHS), make a second follow-up contact. If the DHS response is not received within 15 federal workdays (again, if the follow-up is by mail, allow five additional federal work days of mail time for the G-845 to be received at and returned from DHS), after two follow-ups, contact the Regional Office (RO). Also report to the RO any trend that shows a serious deviation by DHS from the above time frames. The RO will consult with central office.