Is there a CI tool that guarantees no regressions in the branch quality level?
As far as I can tell, you're looking for a tool that will reject commits that break the build—a CI tool probably won't be able to prevent regressions by actually fixing your code, but it can stop you from adding bad code to the repository.

Atlassian has a few interesting applications of Git hooks:


  Server-side pre-receive hooks are an especially powerful compliment to continuous integration because they can prevent developers from pushing code to master, unless the code meets certain conditions – like elite ninja guardians, protecting it from bad code.


If you're using Git, the hooks are very powerful (and there are similar hooks for SVN, Mercurial and other version control systems), and you might find it useful to use them to run pre-commit checks.

The Git documentation has a page on creating a hook to reject pushes if they don't meet a certain criteria which could easily be adapted to this use-case.

However, a lot of people would argue that rejecting commits is a bad idea on a feature branch—you'll just be wasting time fighting against your CI system when the build breaks for some reason, instead of actually fixing the bug. 

On the master branch, it could make sense to reject broken merges, because you might want to ensure it always builds. For a feature branch, you will inevitably break things, and since the code isn't going into production now, it makes more sense just to warn you than actually reject your commit altogether.