a huge amount of fossils that look exactly the same as animals today, frogs
Perhaps this should be handled by an expert. But I think you have your facts a bit off. "exactly the same" implies the same species. I don't think you will be able to site a single case of a species lasting more than a few million years.
Addtionally, why would this be a problem. If the niche continues to exist and doesn't change to drastically the creatures in it may be subjected to selective pressure to stay about the same, not to change.
On your other point Mike, is there any specific point that you think you have come close to holding your own not to talk of winning a point?