Zac,
The best way not to get irritated is to just already have a set number of "tries" she has to go out with you.
For example, I usually give a girl 2-3 opportunities (maximum) to go out on a date with me these days. And I usually only do the 3rd opportunity if I feel like she had a legitimate excuse (or if I had something come up and had to cancel). After that, I tend to just stop texting her because she KNOWS at that point that you wanted a date, so if she really feels like she wants to see you, she'll text you again and try to set up the date herself. At that point, I'll usually go through with it. If not, I never hear from her again, and it prevents me from wasting my time. =)
- Franco