The more links you have on a page, the less likely someone will want to exchange links. That page will look like a link farm to the search engines and have very little value to anyone.
Many website owners hire ‘consultants’ to gather one-way links for them. They will give you a link on a page that is not even seen by the search engines (in many cases) or give you a link on a page that doesn’t relate to your industry (gambling). The result – they get a great themed link and you get crap, nothing, nada because the SE’s don’t see it or look at their page as a huge link farm.
They remove links because that is their purpose – to gain as many one way links as possible. They first pretend to link to you, then months later (when you stop checking) they remove the link and now have YOUR link pointing to their site and no reciprocation. Search Engines like one way links better than reciprocal links.
Hope that helps.