@ehBeth,
To reply to all your question:
1. I don't 'leap to respond' to her panic messages. I may be doing that inside, but my actual replies are friendly yet calm - very much along the lines of your example message. The trouble is the 'let her move things forward' part. She never does that.
2. The 'entertainment' thing was suggested by @jesper in this thread. I think I agree with him for the most part, but it hadn't been clear to me earlier.
3. Other than our initial meetings, and the two occasions later, we have not met. We have talked a few times (5-6) on the phone. The location issue is complex. When we met, we both lived in country A, and she was visiting my city. For a few months then, we met every day. Then she moved to her own city, which was far enough to require air travel. 2 years ago, I moved to a different country entirely, say B. About 4 months ago, she has also, on her own business, moved to B! This is what re-kindled my hopes of a possibility here. Our new cities in country B are now 2.5 hours apart by ROAD. A recent conversation went like this:
Me: 'Now that you're in B, we should meet up!'
She: 'Yes, of course!'
Me: 'Next weekend?'
She: 'I'm not sure, I'll have to see if I can do next weekend.'
Me: 'Okay, let me know. If you can do some other weekend, let me know too.'
She: 'Sure!'
It has been 2 months since, and she has never suggested a weekend to meet up. We have talked in that time, but I didn't bring up the issue for fear of sounding over-insistent.
I don't know if age would help here. I'm 29 and she's 24-26.