Just a note: Different people have different dates. Probably the worst (but usually the first that comes into mind) kind is the "awkward silence in a romantic restaurant" kind of date. This works best in Hollywood movies, and perhaps for experienced seducers who don't feel any anxiety and can easily manage social situations. (For them, this is good signalling, but that's precisely because it is costly. And I don't speak about the costs of the dinner here.)

As an alternative, I would recommend a "doing something fun together" kind of a date. Something that (you can pretend) you would do alone and have fun doing it, too, but today you altruistically decided to offer her an opportunity to join you and have fun too. (Feel the difference? You are not begging, you are offering.) Do a short internet research: is there any gallery exhibition, or music concert, or public lecture, or whatever interesting in your town the next week? (Or simply ask other people what interesting activity would they recommend you the next week. You don't have to explain why you need it. Maybe there is an information service you can call for exactly this info.) Choose something that interests you, so you will be relaxed, and later you can talk about it. She may also feel less pressure on this kind of a date.

(Beware of other-optimization, et cetera. If romantic dinners work for you, just continue doing what works. Although trying something new in addition probably would not hurt.)

You probably already know this, but if your problems are big, you should try a therapist instead of self-help based on an advice from internet. (Although the advice given on this part of internet is usually better than average.)

Doing something is better than doing nothing. Unless you use it as an excuse for not doing more. (As in: "Nothing can fix my problems. What, CBT? No thanks, I tried one exercise based on an advice from internet, and it did not fix my problem. What, visiting a CBT therapist? I am telling you, I already tried an advice from internet, and it did not work.")

That's good! Because it wouldn't be. =]

Uhh. Is the anxiety bad enough that you're sometimes tempted to dump her first just to not have to deal with it anymore?

I didn't offer any particular advice there, only suggested his fears may be rational; but it's an important caveat that merely because a belief is rational doesn't make that belief correct, which I suppose I should have been more clear about.

It sounds to me like the real basis of his concern may be the fact that he's making unreciprocated requests. I have no in-depth knowledge of the situation, so I'm merely hazarding a guess here, but if he's the one arranging all the dates (or whatever), an alleviation of his fears would require her to take a more active role in the relationship. Which may require having a serious discussion admitting his anxieties and the reasons for them. An arrangement where she has to plan every other date, or whatever, might suffice.

I've found a CBT* technique useful for overcoming that sort of anxiety (it's called catastrophising). I write down the situation and my prediction in a spreadsheet. An example would be: Situation - at work, I emailed [girl]; she hasn't emailed back yet. Prediction - She is going to break up with me.

Then when you receive an email back, you write down the outcome in a third column, e.g. received email back - we are meeting up tonight.

Looking back over the spreadsheet, you can see how accurate your predictions have been. I expect they tend to be too negative.

*CBT (Cognitive Behavioural Therapy) has a strong evidence base.

ETA: I hope that explanation is clear - I'm in a bit of a rush right now! I really wanted to explain it though, as it's had an extremely positive impact on my anxiety levels.

Have you dated before?

It sounds like these contact points are natural accumulation points for your anxiety - not so much that you're specially anxious about them.

That said, what sorts of things are you requesting? I'd recommend a shift to make suggestions, or invitations where a 'no' answer can very clearly (even to you) be accompanied by 'It's sweet of you to offer, though' rather than 'GTFO'. If requesting something comes up so often that you've noticed the pattern, and they cause an aversion, perhaps you should avoid making so many requests per se?

So I think a variant of this approach is useful and a variant of this approach is really harmful. If you say "fuck it, she's not important," you'll be conditioning yourself not to care about her or even actively resent her for "making" you anxious. That way lies a lot of badness.

Nevertheless, I do think it's handy to come to terms with the idea that if she decides to break up with you, then it's not the worst thing in the world. It's an admittedly sucky but manageable state of affairs. You will be a finite amount sadder than you were when you were single! And although you have some influence on her decisions, you have no control over them. So think "I have done everything in my control in this situation. Now I will go play video games/exercise/whatever." This is a more detailed, more accurate, healthier variant of "fuck it, she's just a girl."

Fantastic girls are important! But they're not your whole life! But they are also not unimportant! There's a large range in between those two!

Not an advice, just wanted to mention that if you are so worried offline, so to speak, some of it is bound to eventually leak through into the together time, and few people like it when the other person comes across as desperate or clingy. Also note that in most cases people get dumped in person, or sometimes over the phone, not by email/text/facebook status update, so the most dangerous time is probably the first few minutes after you meet up. Hope none of that happens to you.

Do you want advice about whether or not your concerns are rational, or advice on how to overcome these concerns?

And by evidence-based advice, do you want studies? Because I think the specific case may be, well, too specific for evidence-based advice to be useful. Unless your anxiety is more generalized, at least.