That's actually more of a doctrine that is made up by the organization and less something explicitly stated in the book. There probably are some psalms or other references that use the word (translated as) "unchanging", but in context, the original audience would probably not have interpreted it in the same way. Think God's love and power will never fail, not God will literally never experience anything or change. In the 10 commandments story, Moses has a conversation with god and changes his mind.
Yeah, but we all know that no matter how many times that I have already done, tech support won't talk to me until we do it again together