The idea of the technique is to split out code at a different level of abstraction with a clear name communicating what it does, while hiding the details of the how, because you don't need to care about that detail at all to fully grok the code in the calling function.
Where this breaks down is when the code you're trying to split out is not at a different level of abstraction, and how it works is meaningful to the surrounding code in the calling function.
So I think the issue you are seeing isn't with the technique, it's with the technique being misapplied. I think this is likely the only difference between when it 'often works' and 'just as often doesn't' in the code you're working in :-)
The idea of the technique is to split out code at a different level of abstraction with a clear name communicating what it does, while hiding the details of the how, because you don't need to care about that detail at all to fully grok the code in the calling function.
Where this breaks down is when the code you're trying to split out is not at a different level of abstraction, and how it works is meaningful to the surrounding code in the calling function.
So I think the issue you are seeing isn't with the technique, it's with the technique being misapplied. I think this is likely the only difference between when it 'often works' and 'just as often doesn't' in the code you're working in :-)