Opiniatrety

You need an imperfect predicate, it looks to me, since "until" and "while" indicate duration. Thus the perfectly ordinary "It is being until 6."

I want a sign that says "No parking at 6."

I think your disallowed sentences are all allowed if there is context to give "it" a reasonable antecedent, like "the ban on parking." So I guess you're talking about the case where "it" has no antecedent and by default refers to something like "the current situation."

Plenty of phrases such as:
It's metastasized
It's cheap
It's without a father
make perfect sense if "it" has logical context, but seem illogical or to lack necessary information if "it" just means "the current situation." I would place "It is until 6" in this category.

I think "It is while school is in session" is different, and it's harder to say what's wrong with that. It wouldn't be illogical to say, "It's class time," or "It's the middle of the school session."

Maybe it's because "while" implies two things going on at the same time, and if "it" doesn't refer to anything in particular, then there's only one thing going on, school being in session.

How about this:

A: Slow down, we're in a school zone.
B: That rule only applies while school is in session.
A: It is while school is in session -- it's 2 PM on a normal weekday in May.

Richard, agreed about the antecedents; and they're also acceptable in clefts like "It is while school is in session that you can't park here." I was thinking of discourse-initial (antecedentless) uses.

Anders, I don't know, that still sounds peculiar to me.

A Google search on "it is while" yields a bunch of cases where the words bridge two sentences (or something), a few clefts, and this:

If you are a client, the next time you think your agency might not be doing enough for you, or if you feel that the person working on your business might not be giving you the time and attention you feel is needed, review the following list:... 11 p.m. to 1 a.m., 3 a.m. to 5 a.m. and the minutes in between: This is my least favorite time of day to be thinking about media planning and buying, but it is often an inevitability. At first, it's near the end of the day, after working, working some more, having dinner, and then a glass of wine or a drink or two to chill out. But then it is while you're in bed trying to fall asleep. Then it's when you wake up to go to the bathroom and can't help but start working on your client's problem. And when you wake up… there's the client's business, sitting right at the top of mind!

I do believe that is an example of what we're talking about, but I have some trouble telling what he's saying.