Whenever you perform testing, particularly UI or performance testing, you will get noisy results. Reliability is not perfect, and there will always be failures that are not due to bugs in the code. You shouldn't let these false positives cause you to ignore failing tests, and although the easiest course of action may be disabling them, the correct thing to do to make them more reliable.
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The scientifically minded know that there is no such thing as a perfect filter in binary classification, and always look at the precision and recall of a system. Knowing the rate of false positives and negatives is important to get a good idea of the accuracy and tradeoffs involved.
To avoid testing fatigue, it can be helpful to engage developers and instill a responsibility to fix failing tests. You don't want everyone thinking that it's somebody else's problem. It should be easy to see who broke a build by the commit in version control, and it's then their job to fix the failing test (and...