So here's a new problem I'm faced with. I've been contracted to do some SEO on a site which has around 80 outgoing links over 8 categories within the same niche. All of the links were generated from a reciprocal linking script on the site which verifies a link back to us etc. but out of those 80 sites, only 2 link back to us now. So my question is; If I remove 78 of the links, can it have a negative effect on the current ranking of the site?
No - it shouldn't. It would actually help your page since only two links are going out. The 78 links may hurt the other sites a little though.
Reciprocal method is talk of past, even google doesnt recommends it. Prefer three way exchange or just go with one way links.