Is there a limit to overriding final static field with Reflection?

I have been faced in some of my Unit test with a strange behaviour with Reflection on final static field.

Here a example illustrating my issue:

I have a basic Singleton class that holds an Integer

public class BasicHolder {
    private static BasicHolder instance = new BasicHolder();

    public static BasicHolder getInstance() {
        return instance;
    }

    private BasicHolder() {
    }

    private final static Integer VALUE = new Integer(0);

    public Integer getVALUE() {
        return VALUE;
    }

}

My test case is looping and setting through Reflection the VALUE to the iteration index and then asserting that the VALUE is rightfully equal to the iteration index.

class TestStaticLimits {
    private static final Integer NB_ITERATION = 10_000;

    @Test
    void testStaticLimit() {

        for (Integer i = 0; i < NB_ITERATION; i++) {
            setStaticFieldValue(BasicHolder.class, "VALUE", i);
            Assertions.assertEquals(i, BasicHolder.getInstance().getVALUE(), "REFLECTION DID NOT WORK for iteration "+i);
            System.out.println("iter " + i + " ok" );

        }
    }

    private static void setStaticFieldValue(final Class obj, final String fieldName, final Object fieldValue) {
        try {
            final Field field = obj.getDeclaredField(fieldName);
            field.setAccessible(true);
            final Field modifiersField = Field.class.getDeclaredField("modifiers");
            modifiersField.setAccessible(true);
            modifiersField.setInt(field, field.getModifiers() & ~Modifier.FINAL);
            field.set(null, fieldValue);
        } catch (NoSuchFieldException | IllegalAccessException e) {
            throw new RuntimeException("Error while setting field [" + fieldName + "] on object " + obj + " Message " + e.getMessage(), e);
        }
    }

}

The result is quite surprising because it's not constant, my test fails around iteration ~1000 but it never seems to be always the same.

Anyone has already faced this issue ?