It's hard not to give it thought because it messes with your head, but your goal should be to not give it any thought because there is little you can do about it. You can try to take it as an indicator of interest (or lack of one in this case), but there isn't much you can do but to force her to take action, and to back off a bit yourself. When a girl slows up in her responses to me, I do the same to her, if not even more. My responses to her become increasingly short, and increasingly more time between texts. I won't initiate texts with her any more than once a week and if I feel like she's really lost interest, I won't initiate at all.
I'm actually in that exact situation myself right now. This girl I've been on/off with for almost six months now broke things off with me a couple months ago. We both went no-contact. Then after a month, she reached out to me. I didn't even have to invite her out because she invited me out in her initial text to me. But I did set the specific date/time/place/activity. After that agreement to hang out, we didn't text as often as we used to - maybe once every 3-5 days. After the date, and hooking up, we text even less, but she does initiate and when she does, I invite her out on a date. She always says yes. But these days she is taking 12-24 hours to respond (and by that I mean, even if she initiates text, I may respond in 1 hour or 12, but she never responds faster than 12 anymore). Really nothing you can do about it. If she's losing interest then there is no action you can take to regain her interest other than take away your time and attention to her.
I am curious to hear what
@Glassguy and others have to say about this though.