I get first time syndrome almost every time I have sex with a new girl. Thing is though that I can get hard and go for ages, just not cum. Usually lasts for a few encounters until I feel comfortable, then I cum and everything after that is all good. Does mean that the first few times can be awkward though...
"I came, how come you didn't? Wasn't it good for you?"
"Oh it's just one of those things, sometimes I don't cum the first few times I sleep with a girl, you were great though and I really enjoyed it!"
"But if you enjoyed it why didn't you cum?! Guys always cum!"
"Oh... Ok... Ummmm..... How can I convince you you're not shit in bed?"
It's like having to explain the female orgasm complex from a male perspective... BUT BEING A MALE!
Anyway, my point is that his anxiety will only go away when he feels comfortable. That might take time or be a particular location or thing that you do or even a supplement/drug he takes. Regardless, until it happens every time he encounters the situation when he's supposed to be hard he won't be thinking "oooh, this is exciting" and get hard, he'll be thinking "I'm supposed to be hard, why aren't I?" and won't be.
He's being controlled by what he expects himself to be able to do in the given situation. Either take that choice away with a supplement or something, or (something I think would be better) remove the meaning of the erection. Try getting him hard in places or situations that aren't going to lead to sex. Even if they could lead to sex (bus journey home, hand runs up thigh etc) don't let them, just leave it at that. IMO he'll realise that him being hard isn't solely to please you sexually, you just like making him hard sometimes. When he knows you can make him hard outside of the situation his anxieties won't matter so much anymore as his body will be programmed to expect arousal from you.
It's all a placebo. His mind expects him to not be able to get hard in that situation and expectation is a very powerful thing. Sorry, essay over and hope any of that lot helps!