Meaning – What Is the Meaning of ‘Every Other Time’?

One idea that can make the sentence more acceptable is in the understanding of "everything". If you consider the statement to be "no matter what object you pick, you will find that it has changed since the last time you looked at it", then yes, you may be able to say "Robusto's name has not changed since the last time" or "this piece of paper has all the same properties as before".

However, if you interpret "everything is always changing" in the sense of "you will always be able to find at least one thing that has changed since last time", then it is much more readily apparent that this is the case. Robusto might not have changed his name, but he got a haircut, or he has different shoes on. The paper is exactly the same, but there's a pen next to it that wasn't there before.

So, it's not that every item is always different, but that some item is always different, and thus the set that contains all items is different.

You've answered your own question: every is a determiner which is used to introduce the frequency of the action. The difference is that some actions are rare or infrequent or the period isn't strictly known.

• every day : once a day
• every 5 minutes: repeats with a period of 5 minutes
• every once in a while: repeats with an unspecified period (a while)
• every so often: repeats with an unspecified period
• every once in a blue moon: repeats on rare occasions when the moon is blue; the time period is the amount of time between blue moons. (This usage is never meant to be taken literally - it just means "rarely").

Just because "once in a while" is a phrase doesn't make it function like less of a noun than "day" or "5 minutes". In all of those cases, the word or phrase after "every" represents a time period.