Some websites will show your partial backlink profile but they will never be able to show your entire backlink profile.
I have websites that yahoo siteexplorer used to show 30k+ links where ahrefs.com (probably the most accurate free backlink profile checker) 2.2k links. This is a website that is almost 6 years old and I have not created many new links this past year.
It is not a question of time, it is just that these websites do not have the resources to reliably track this amount of information and no search engine wants you to see these figures as it would just help you to see what works in gaming the search results for your benefit.
Really there is no good reason why these figures are of any use any more, their usefulness was always questionable in my book but now the figures are not representative of what the search engines see or take into consideration so they are largely irrelevant. The only time they are really useful is in seeing where your competitors are getting their backlinks.
You can clearly see the links created by NHSEO by
exporting the list of linking pages or by running the Link Checker, both of these methods will at least show you the links that you have created. If you have left the "Ping Confirmed Links" option checked then each time you have a link auto-approved the major search engines will be automatically notified and will notice them quickly.