Maybe your unit's are too big. Unit tests are tricky because it's about coming to a personal and team agreement on what a 'unit' of functionality is.

I find the same issue in throwing away tests when I'm writing small scale integration tests with junit. Usually I'm mocking out the DB and a few web service calls. So those tests become more volatile because their surface is exposed more. But smaller level, function and class level tests can have a really good ROI and they do push you design for testing which makes everything a bit better imo.