There are two common issues when it comes to pagination and links:
Firstly a link may appear on more than one page, because the content is used in different locations within a website. For example within different categories, or taxonomies. This can be a particular problem when choosing to disavow links on a URL basis, rather than at domain, subdomain, or folder level.
The second occurrence of pagination being an issue, is that sometimes a link may be ‘nomadic’ in nature. This means that the links don’t stay in one place, and thus can make it hard to identify if a link still exists on a site, or you have found them all. For example when the link data being used to review a site is collected it may state that the link is on page 2 of a category. However by the time the link is actually reviewed, more content may have been added to that category, causing it to be ‘bumped’ to page 3.
So if you visited the first URL below it would seem the link has disappeared, but in fact it has just moved to the next page.
Page 2 (domain.com/category-x/2/) >Page 3 (domain.com/category-x/2/)
Example of a Paginated Link
A directory listing may have been added to more than one category, and because a backlink appears within the content used on the category it is thus paginated on different pages of the directory.
The link data you are using may show that the link is on page 1, however the link data is out of date and the link was pushed onto page 2.
It may appear that link(s) are no longer on the website when you visit a page using 3rd party link data. This is because the link data is simply out of date, because the link has ‘migrated’ to another page on the website.