Actually a link page does not have a page rank this may happen due to several other reasons as follows:
1. Your web site’s links page may be new and is waiting for PR in the Google toolbar. This could be the simplest reason.
2. Another reason is dynamic linking, if it is going on. You can find out whether this is the reason or not by checking html code which must have words no follow if it is true.
3. If your link page does not have any link pointing to it from another page, then also it may suffer by page rank.
4. One more possible reason is deep link navigation of the website. Generally webmasters insert the link to their links page very deep actually they do so because they want it to be viewed only by search engine spider.
5. Sometimes one site has number of reciprocal associates, as links are often divided among all the partners. That creates a problem to search engines because they have to search link by link.
6. A serious reason can be the existence of a robots.txt file for link exchange purpose. This file prevents the search engines robots from visiting the link page, and so your site does not achieve page rank.