Imagine that you are INTERESTED in a girl with a lot of fears and she needs tons of comfort to trust you and this is gonna take a long time. How you don't let the line go slack? How do you keep her interested in you? How often you get in touch with her to keep her interested in you?

This is going to vary widely depending on the girl, the situation, and your interaction with her. Impossible to say. But general follow up game principles apply.

I'm wondering about this too. I had a first date on Saturday that I thought went well, but due to me moving this weekend, plus the girl being on the other end of the city, the earliest I can get her out on a second date is next weekend. Thoughts?

Leo, Keeping a girl interested and working on building trust are not really related. Either she is interested or she is not, that is all up to her. You can present yourself with your best foot forward and do what you can to offer interesting conversation, a fun time, etc., but at the end of the day whether she is physically attracted or likes your personality, that's on her. Making her feel secure and comforting her about your interest is on you. If you know this girl needs alot of attention, give it to her. Call her everyday, or at least text. Everyday.
Matty, I say you plan your second date now, even if it is way far in advanced. It will give her and you time to look forward to it and get excited. Shit happens, we all know it, I'm sure she will understand. But if you wait until next week to set something up, she might already thing you're not interested at that point. Make set plans for a date and then continue to maintain communication throughout the week. Close to your date, let her know that you are looking forward to the date yadi yada.