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Once you have a blackmark against your name for a particular page can it ever redeem itself? Or should I start again with a new page?
You don't need to do anything special to get Google to look at the page again. Just keep working on the things we know Google likes, and your changes will get picked up in a future update and evaluated according to the algorithm operating at that time.
I think that it is a bit too Keyword Dense
Google's webmaster guidelines [google.com] don't make specific references to penalties, but do speak about "deceptive or manipulative behavior." A few extra keywords on a page aren't quite deceptive or manipulative; it's probably just that the search algo determined that other pages better meet the criteria.
I have now sorted this out, redone all parts of the page and now I think it is better.
Tweaking was the right thing to do. Since you've already made the adjustments your best bet now is to wait a bit and see what happens during the next couple of updates. You should also check to see if the page is indexed by Google:
allinurl:www.yourdomain.com site:www.yourdomain.com
If not, make sure that the page is reachable by the spiders.
Jim