Hi Steve
If Google is saying there are still a few more links, then it might be an idea to manually review a few others that you haven't disavowed. I find the LinkDetox tool very useful for this. It's free with a tweet and will tell you if a link from a site is toxic (the site is deindexed) or if it's suspicious (and why it's suspicious). You still need to use your own judgement on these, but it might help you to find the extra links you're talking about.
However, there is a chance you have gone and disavowed every bad link, but still got the rejection. In this case, I'd keep trying but make your reconsideration request more detailed. Create an excel sheet and list the bad URLs and/or domains and give a reason explaining why you think they're bad links. Then provide information on how you found their contact details. If there are no contact us pages, check the whois registrar's email. After that, say when you contacted them (give a sample of your letter to them too), and if they replied, along with a follow up date if you got silence. If there are no details in the whois, explicitly mention that there are no contact details and so you have proceeded straight to disavowing.
Then list the URLs you've disavowed (upload the .txt file with your reconsideration email). You've now told Google that you've found bad links, why you think their bad (also include how you discovered them), that you've contacted the webmaster on numerous occasions and, if no removal was made, you've disavowed as a last resort. This is a very thorough process and uses the disavow tool in the way that Google wants us to - as a last resort to an unresponsive or anonymous webmaster.
Please forgive me if you've already done all this and it seems like repetition. I only mention it because I've found it's best to be as thorough as possible with Google in these situations. Remember, a reconsideration request is manual and if they see that you've gone through all this effort to be reinstated, you've got a better chance of being approved.
Keep trying, mate. It can be disheartening, but if you think it's worth the time and effort, then keep going for it. I would bear in mind the alternatives, however, such as starting fresh on a new domain. If you find yourself going round the bend with endless reconsiderations, sometimes your time, effort and expertise can be better put elsewhere.
All the best!