It depends on the input string, doesn't it?

No, I've copied those tests from Java test suite, if you see other thing in sample tests, click reset. These should be the sample tests:

	@Test
	public void BasicTests() {
		System.out.println("****** Basic Tests ******");
		assertEquals(3, Persist.persistence(39));
		assertEquals(0, Persist.persistence(4));
	  assertEquals(2, Persist.persistence(25));
	  assertEquals(4, Persist.persistence(999));
	}

You're confusing the input of one test with the expected value of another.

    assertEquals(3, Persist.persistence(39));
    assertEquals(4, Persist.persistence(999));

Those are the assertions and you can see they're both ok.

9*9*9 = 729 (1)
7*2*9 = 126 (2)
1*2*6 = 12  (3)
1*2   = 2   (4) 

The tests are ok. This case is even explained in the kata description.