If the semester they failed to report you as enrolled was continuous, yes, you shouldn't have begun your 6 months grace period yet. If there was a gap and you went back to school it was your responsibility to ask for the in-school deferment even though sometimes it's automatically granted.
I would start by gathering the papers proving enrollment, such as maybe your transcripts with grades to prove you finished the semester. Submit these to your servicer, in writing (mail or fax, without your phone number), with an explanation of the problem. Let them reply in writing. If you make a phone call or send mail log the dates and people you had contact with. You should also get copies of your bills and any written notifications they sent during the time of the lates and your enrollment.
If you do not have success dealing with your servicer, the next step is the student loan Ombudsman. If you don't get a good resolution there, go to the Consumer Financial Protection Bureau and file an online complaint there. Tell the story in detail and include all the paperwork and information from above. That had the most success for me. It seems like a hassle but I would do it if I had lates that weren't my fault. Servicers often avoid accountability. I don't think federal student loan lates fall off after 7 years. You might want to check.
