I've had a similar problem with two of my videos (which did use copyrighted content, but did so for the purposes of parody and satire and so constituted fair use). There is a process to dispute a Content ID match, but YouTube allows the Content ID claimant to reject the dispute and reinstate the claim without providing any reasons.
This is contrary to YouTube's stated policy which is to require a claimant to lodge a DMCA takedown notice if a Content ID match is disputed. (I've extracted the relevant policy below - there's also a reasonable article in Wired about the issue here http://www.wired.com/business/2012/02/opinion-baiodmcayoutube/
I wrote to YouTube pointing out that their actions were inconsistent with their stated policy. Unfortunately YouTube fobbed me off - but they did provide me with the contact details of the Content ID claimant. If you really want to get rid of the ads, request the contact details of the claimants from YouTube (firstname.lastname@example.org) and email them directly.
The whole situation is deeply unsatisfactory but I hope this is of some help.
The relevant page in the Copyright Center addressing Content ID matches contains the following statement:
"If you feel that your video has been misidentified by the Content ID system, you can dispute the identification. This involves filling in a short form listing the reason for your dispute. We then notify the content owner whose reference material was matched. The content owner will then review the match. If the content owner disagrees with your dispute for any reason, they will have the option to submit a copyright takedown notice, which will result in the disabling of your video and/or penalties against your account. To avoid penalisation, only submit legitimate dispute claims."
That statement is consistent with the policy articulated in this YouTube blog post which states:
"When you receive a notice in your account via Content ID, we tell you who claimed the content, and direct you to a form that lets you dispute the claim if you so choose.
If you believe your video is fair use, check the box that reads "This video uses copyrighted material in a manner that does not require approval of the copyright holder." If you're not sure if your video qualifies, you can learn more about fair use here.
Once you've filed your dispute, your video immediately goes back up on YouTube.
From this point, the claimant then makes a decision about whether to file a formal DMCA notification, and remove the content from the site according to the process set forth in the DMCA."