Problem
Its quite a common problem I would like to think. Adding new code translates into regression - existing test cases become obsolete. Dependencie
The best tool you can find for your problem is actually not a tool, but a practise. I strongly suggest you read about Test Driven Development (see Lasse Koskela's book), and Specification by Example (see Gojko Adzic's books, they're great).
Using these practises will fundamentally change two things:
The reason why I find this relevant to your question is that your scenario hints for the exact opposite role of the tests: people will perform changes in code and they'll then think "oh, no...now I have to go figure out what I broke in those damn tests".
From my experience, tests should not be overlooked or considered "lower grade code". And while my answer points to a methodology change that will only have visible results on the long run, it might help avoid the issue altogether in the future.