You only need to make one mistaken assumption to introduce non-determinism. Say you wait for the page to load, then click a button, is that valid? Sometimes it is, but some UI frameworks might render the button after the page reports being loaded. Your test will generally pass regardless, but mysteriously fail periodically.

You also tend to never achieve full reliability because the environments aren't entirely stable. Almost everyone sees more "random" failures on old IE versions. Poor over-stressed IE9 running in a VM will have a bad day and your test will fail.

If multiple threads are running, the order that the threads are scheduled is nondeterministic. And if there are any timeouts anywhere in the code, the result is nondeterministic due to the nondeterministic method that the kernel will schedule the process and environmental effects of whatever other programs are running at the same time or recently ran.

Some examples I've seen: Changes in browser code or DOM handling can break the test. Memory issues from having too many instances of Chrome can break the test. There are a lot of factors at play that are slightly difficult to control for

Not sure if this paper helps answer your question: http://alandix.com/academic/papers/nond90/