1. Hardly a day goes by when I didn't think about her.
2. Hardly a day goes by without my thinking about her.
Sentence 2 is understood without any difficulty but sentence 1 has something usual to me.
Sentence (2) is fine, but you are right that there is something wrong about (1). What is wrong is that there is a conflict in the tenses. "Goes" (present tense) should be "went" (past tense). You can say:
- Hardly a day went by that I didn't think about her.
- Hardly a day goes by that I don't think about her.