So I'll go for the answer on this and list methods I would try expecting one would work...

That is (dare I say) 100% a glass dome that is essentially threaded.

There are two main approaches to removing it, each with their challenges.

1. Convince the glass to be displaced (or)
2. Manuever the fixture as a whole.

In reverse, but a mix of the two can be useful:

TWO:

This might be easy enough, but it runs the risk of damaginf the ceiling paint, the dome, or the fixture. But if you plan on replacing it, it might be a chosen method. Read through and decide if it is worth trying, if not, skip and go to ONE below.

• Using a paint scraper (or two), or a flat blade screw driver (or two): Pry on adjacent sides, and work your way around.
• Only pry no more than an inch or two of leverage (so no more than say just shy of 1/4") between the ceiling and the top of the metal meeting the ceiling. This is going to be a judgement call, but overdoing it will result in breaking the dome and even deforming the fixture.
• Once some clearance is created one of two things can happen; moving the fixtures framing, has created an air gap that wasn't there previously and also changed the "stuck" friction points holding the dome in place. So try the basic removal of the dome again (you may choose to do some of #1 in this attempt). If no go, continue...
• Make a mental note or a pencil mark of where the fixture was originally against the ceiling. Rotate the entire fixture counter clockwise. You should not need to turn it more than a few inches. It may drop off, so be sure to support it while trying this. If it doesn't seem to be moving free, give up and move on. Return it position to where you started.
• When all is said and done you are going to want to loosen the fixture and make sure the mounting plate is not toqued too tight, but also not loose. This is likely one of the reasons you are in your current predicament.

ONE:

This is a better choice if you intend to re-use the fixture, but still presents its challenges and may end up in needing a new dome, which nearly certainly results in needing a new light since finding an original dome will be more challenging than it is worth.

The thing is, the dome is only held on by 3-4 dimples in the metal frame which fit into a slot on the glass. If the frame was over torqued, or the temperature of the enviroment has changed from when it was installed, the dome can really get "locked on" there. The problem is there is no real way to grab on to it and not damage it.

You have two options, one, lubricate it/heat it up, or create a handle to work with. I vote for the latter as I commented above. I googled and found this link this morning which is similar to what I was suggesting. Give it a quick watch and read below:

https://www.youtube.com/watch?v=vXHylBQzrIs

His approach is similar to what I was suggesting but:

• Place a long piece of tape on one side (call it the top for now), with a long leader hanging off to the left.
• Place a long piece on the "bottom" with a long leader to the right It would look like this if you looked face down onto the dome:

{

               /````````
  A||||||||||||||||||||  
             (            )
            (              )
             (            )
                ||||||||||||||||||||B
               ,,,,,,,,/

}

Now, just like pulling pigtails in 2nd grade... ok, not quite, but you get the idea... Grab A and pull left, grab B and pull right, do this simultaneously. Its a good idea to have another person supporting the dome so it doesn't become a UFO.

Another note to be made here is to push up and pull down on the dome before, during, and after this attempt. In fact, gentle tapping with your bare hands can help. The whole idea is to get the two surfaces to break free and friction and months/years of dirt, moisture, grease, dust, has helped create a dry glue.

Lastly, try a humidifier for a few hours, the heat and moisture could help. But it can make a mess, and of course just secure power to stay safe. It's a crazyidea. but these should lend themselves to success.

Screw on glass domes are junk.

Good luck.

I will accept @noybman 's answer for his detailed exposé. I wanted to share what has happened here to replace the light bulbs in the stubborn fixture.

We applied long strips of Gorilla tape to the fixture globe with "handles". This only resulted in the whole fixture twisting. Finally rotated the whole fixture so the the screws that hold the metal plate up to the ceiling twisted out of their key hole slots. This allowed the whole fixture to be lowered down from the ceiling.

I disconnected the electrical wires from the fixture so that we could inspect the fixture on a table. I was able to flex the metal part of the fixture and with two sets of opposing Gorilla tape handles on the globe and on the metal bezel we were finally break the globe loose From the metal part.

Close inspection revealed that sometime in the long past some water had gotten into the space between the upper globe edge and the metal surface. Rust had formed between the glass and metal essentially locking into place. It seems that flexing the metal part aided in breaking this lock to some extent.

After cleaning up all the parts, reconnecting the wires and reinstalling the fixture everything is operational again.