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I can't see anyway to stop the bad links being built or to get them removed.

I would suggest the following:

1) Continue to build good quality links to the site.
2) Contact Google using webmaster Tools and pray for a manual site review

As a general observation, i've found it very difficult to manipulate search results based purely on links to a site are you sure this is whats causing the problem.

I believe that Google would only devalue any potential value the links may have rather than penalise the site they are pointing to, they can't have people disabling competitors in this way.

In the past you could Google bomb someone's site with bad links. I know, it happened to one of my sites and it took an email to Google to get this sorted out. How do I know bad links were the cause? Because I retaliated with the same tactic and punished a few of this guy's sites.

However, that was a few years ago and Google seems to have closed that loophole.

Now if your competitor built thousands of links to that site in a short period of time there may be a slight chance the site got nicked, but I don't think that's the case here. How much did the site lose in the rankings?

My guess is that some of the previous links you built to the site became devalued. That happens all of the time, especially if the site is not considered an authority site.

It will be better if you will manual contact the Google itself. I too can't see the stopping of bad link in your site. And when the competitor uses software like X-rumer to create automated links than there are many links created that are generally known as spam.So it will be better if you contact the Google itself.
Best of Luck!!