The meaning of the three terms "noch", "immer noch" and "noch immer" differ, so when changing from one to the other you might get a different meaning.
Generally the combinations of "immer noch" and "noch immer" imply that the situation was expected to change and/or that one is not happy with it.
See the examples given by @elena.
Although most of the time "immer noch" and "noch immer" can be used interchangeably , those two can have a slightly different touch depending on the context (or the lack of it).
If you have some context in the same sentence or maybe a preceding one the two are interchangeable.
Obwohl er sie schlecht behandelt hat, liebt sie ihn noch immer/immer
But if it comes up on it's own, "noch immer" has a negative connotation.
Sie liebt Ihn noch immer.
Does imply one hoped this wouldn't not be the case (e.g. because he is a bad person).
Sie liebt Ihn immer noch.
This on the other hand would be said if there is some doubt about it, but one hopes it is the case (e.g. a couple has been together for a long time or lived through some difficult times in their relationship)
It gets a bit clearer if a question is asked.
Liebst du mich noch?
Liebst du mich immer noch?
Liebst du mich noch immer?
The third one does not work at all.
The above mentioned differences do not necessarily apply to every situation.
If one is talking about the weather they are interchangeable.
Es schneit noch immer/immer noch.
Depending on what you're talking about, the sentence can change.
If we ask the question "Are you still there?" as an example, you can be talking about the place "Are you still THERE?" or about the presence of the person "ARE you still there?"
In German the question is built differently depending on what you are talking about.
If you want to know about the presence of the person it'd be:
Bist du noch da?
If you expected the person to leave:
Bist du immer noch da?
When talking about the place it would be:
Bist du da immer noch?
Another example would be the working place.
If you just want to know if somebody is still working at the same place one would ask:
Arbeitest du noch da?
But if the person talked about leaving that particular company, one of the following questions would be used:
Arbeitest du [etwa] immer noch da?
Arbeitest du da noch immer?
"Da" is standing for a known place and would be translated with there.
One thing that applies to all of the above examples is that you can tell by the word order what would be empasized when speaking about it.
That's also why I would say "noch immer" can have a negative touch if it is used without context.