H1B is filed by employer, so they should be the one to contact USCIS on your behalf. I know given the case status USCIS rep. might talk to you, however, thier access to the system is limited and they chances are less they will go above and beyond that is required in your case.
Please see the USCIS press release below,
USCIS Update: Case Status Inquiries with the Service Centers
WASHINGTON - U. S. Citizenship and Immigration Services (USCIS) has issued instructions on making inquiries with the agency's four Service Centers. Customers, community-based organizations and liaison groups should follow this guidance when inquiring about case related issues. This new process standardizes customer service and streamlines processing of customer inquiries at USCIS Service Centers. The step-by-step instructions are as follows:
Step 1: Contact the National Customer Service Center (NCSC) at 1-800-375-5283. The NCSC can assist customers, community-based organizations and liaison groups with case related inquiries. Before calling the NCSC please have available your receipt number, alien registration number, type of application filed and date filed. During your call we recommend that you take note of the following information:
-The name and/or id number of the NCSC representative
-The date and time of the call
-Any service request referral number, if a service referral on a pending case is taken
Step 2: If more than 30 days have passed since you contacted the NCSC and the issue has not been resolved or explained you can email the proper USCIS Service Center to check the status of your case.
-California Service Center:
csc-ncsc-followup@dhs.gov
-Vermont Service Center:
vsc.ncscfollowup@dhs.gov
-Nebraska Service Center:
ncscfollowup.nsc@dhs.gov
-Texas Service Center:
tsc.ncscfollowup@dhs.gov
Please note: Emails should be sent to the Service Center that has jurisdiction over your case. The receipt notice will indicate EAC for the Vermont Service Center, SRC for the Texas Service Center, LIN for the Nebraska Service Center, and WAC for the California Service Center.
When contacting the Service Centers by email you will need to provide the information outlined in Step 1. If the NCSC did not issue a service request after your call, please indicate the reason the NCSC representative did not issue the request.
Step 3: In the event you do not receive a response within 21 days of contacting the appropriate Service Center, you may email the USCIS Headquarters Office of Service Center Operations by email at:
SCOPSSCATA@dhs.gov. You will receive a response from this email address within ten days.
I hope this above info. will help you if you have not got the answer back from USCIS.
Thanks,
Zia