On Semper Invicata you can only lose Dalia's path in prison due to low affection points. This is actually quite common, Dalia's path is easily lost early on. I guess you have to retrace your steps if you want to retain her path. Let me help you out a bit...
EARLY GAME SPOILERS
You need to do at least 4 of the following:
- When meeting the sisters for the first time, let them go without asking for anything in return
- Agree to do Nancy's chores, then stay in the bathtub when Dalia comes in, then tell her she's beautiful
- On Ekabar, attack Con right after Dalia says the codeword "moron"
- Stay with Dalia during the first Thanatos encounter
- Say that you prefer Dalia's brownies instead of Alex's bagels
- Offer Nancy to make breakfast in the morning before going to the gym
Depending on where you missed these opportunities, you don't have to rewind too far, hopefully. If you want to avoid this kind of thing in the future, I have a novel walkthrough mod that might interest you.