The NCB stays in waht is called abeyance (poss spelt wrong!) until either liability is admitted, OR the outlay is recovered from the third party insurers.
We allow the NCB again as soon as liability is admitted, but some insurers will wait for the outlay to be reimbursed -there is no set way of doing this.
There is a possibility that the third party insurers have ongoing enquiries due to a number of reasons which has meant that they have since retracted their admission of liability (although I note the other driver admitted liability, that makes no real difference as it is us, the insurer, who actually makes this decision).
As for his insurer not reinsuring him, even a non-fault claim can affect the rating factor - statistics (apparently) show that if you are involved in a non-fault incident, then you are more likely to be at fault for the next one. However, it could simply be down to the fact that he has a claim logged against him and no NCB that deems him a poor risk - not good business practice though if that's the reason.
As suggested, it may be worth ringing his insurance and the other company to see what the issue is. The circumstances seem fairly clear cut, but like I say they could be an issue on the third party side - could have undisclosed convictions, claims, been drink driving, etc.
However, before anyone points this out, even the above wouldn't necessarily stop them admitting liability or reimbursing the outlay, although it would cause delays whilst investigations are underway