I think the reason may be that the lifecycle of sperm is about 3 months, so if they leave some time between samples if the last one was a fluke or just a bad sperm cycle, then there has been a chance for new sperm to grow.
Since we've had our diagnosis, I've asked DH to quite smoking (he didn't smoke much anyway) and reduce his alcohol intake (also small). He's on a high dose of vitamin C and zinc, as they're supposed to be good for sperm development, and we've changed our diet so there are no takeaways or processed food. I don't know if it will help, but it won't hurt him. DH is also overweight, and I wonder if this is a cause too. Could it be that his belly sits over his man parts when he sits (and he spends all day sitting), and his thighs touch at the top, are creating an environment that is too warm for his sperm? I know, there are plenty of men who are more overweight than DH, but it may just be that he is more sensitive to these things.
Where men aren't producing any sperm at all, you could look into his history. Did he have mumps, or undescended testicles as a child? DH didn't suffer from either of these, but he did suffer from an immune disorder which took a long time to recover from, and even a virus can arrest sperm development. DH also suffered epilepsy, and took high doses of Sodium Valproate for a long time as a teenager. Studies have shown this can lead to Azoospermia, but we're wondering if we can prove that.
As for free treatment over here, it really does depend where you live. The guidelines state you should be entitled to 3 free cycles, but that is rarely the case. And waiting lists are so long, that if you can afford it you might aswell go private.
Our PCT has just messed up with our referral to the Urologist for DH, so we are at square 1 with that. We can't even have the investigations carried out by our health care policy, as DH hasn't been covered by them for 3 years.