Lost Foreign Passport needed for Citizenship

I am writing on behalf of my grandmother who is attempting to file for citizenship. I'm not certain if she will meet the "continuous presence" and and residency requirement required for US citizenship because she lost her foreign passport. She did obtain a new one but it has no dates reflecting her initial date of entry (9/27/03).

Her new passport reflects dates only from 2007 to current. She has no independent recollection of the exact dates she arrived in the US and departed the US in the past 5 years and 7 months. She would often go back home every year since initial entry into the US for 6-8 months at a time to visit loved ones back home (I'm aware of the 6 month departure limitation as well). How does someone fill out form N-400 without all the exact dates? Is there somewhere one can obtain records of this entry/exit to satisfy the above requirement? Please advise if efforts to file at this point are futile. Thanks a million!