Hello Nikolai,
What's the format of the hyperlink?
e.g. absolute (i.e. including the domain name), site root-relative, page-relative, etc.
How did you create the hyperlink?
e.g. using the hyperlink button in a Text Component, manually inserting the HTML code for the link, etc.
When you create a site root-relative hyperlink using the Hyperlink button in a Text Component, and then use the Content Finder from the Hyperlink dialog to find and select the page, this should ensure that the link stays updated.


(Source of images: Boston College)
I hope this helps.
If it does not, we may need more information from you to sort this out.
e.g. if/where is LiveCopy used? nested launches or just single one? scope and other options selected during promotion? etc.
Kind regards,
- Carey