Is it normal that I keep burning my seasoning off my cast iron?

No, this isn't normal. A little flaking, perhaps, when you go over 600°F, but 500°F shouldn't do anything. It shouldn't even smoke.

Something is wrong with the seasoning on your pan. From the fact that its smoking, I'd guess its not sufficiently baked on. Alternatively, maybe the pan wasn't clean when you applied it.

If its just not baked on, I'd remove all the flaking bits (with some harsh scrubbing, sand paper even), clean it thoroughly, then bring it to around 300°F (stovetop or oven). This will make sure it is completely dry. Spread a thin layer of high-iodine value oil (flax seed is great, soy is pretty good and cheap and easy to find: look for the bottle that just says vegetable oil and check the ingredients, it's probably soy). Spreading is easy with a paper towel.

Next, toss into a very hot oven, 400–500, smoking is expected. Bake for 90 minutes, then turn the oven off. Allow pan to cool with oven. Once its cool, touch it. If its at all tacky, put it back in the oven, and bake for another hour (once again, allowing to cool with oven). It should be a shiny black at this point, and not at all tacky.

You can repeat the process to add more layers. Two should be reasonably non-stick to start cooking on.

If it still peels off after this, you're probably going to need to strip the seasoning and re-season the pan, after stripping it to bare metal. See What's the best way to season a cast iron skillet? to season it from bare metal.

Seasoning is part polymerized oils, as people have said, and part carbonized oils. These are oil molecules that have actually burned and blackened. It's the matrix of polymer (plastic) and char that gives you the blackened, stick-resistant qualities. It's also why the seasoning should be stable well beyond the smoke point of the oil—you had to get it past the smoke point to create the seasoning to begin with.

Flax oil is indeed good, but any oil that's high in polyunsaturated fat will polymerize easily and do a good job. Look for refined, high heat oils. If they list the smoke point, so much the better. To get a quick seasoning, I set the oven 25 to 50 degrees higher than the smoke point, and apply thin layers of oil (usually the safflower oil I keep on hand for sauteeing) with tongs and a paper towel. Yes, there's a lot of smoke.

There is of course a point at which the seasoning will burn off. The self cleaning cycle of an oven is typically around 900°F and will turn your seasoning to ash, leaving shiny virgin cast iron behind. I've seen a grill pan used on a commercial burner at a restaurant that didn't have a hint of seasoning on it ... it spent most of every evening sitting over a 20,000 btu/hr burner.

My home stove puts out barely more than half that power, and is not capable of heating a pan enough to burn off a proper seasoning. I can get pans maybe a little hotter than 500F. Hot enough to form seasoning, but not enough to damage it.

You are using the wrong sort of oil

Use an oil with a strong and dry polymerisation effect, e.g. Flax (Linseed) oil, tung, even soy oil

Canola, olive etc do not form very hard polymers, and often remain tacky

If you have a pan with layers of flaky soft oil, just leave it on the high heat until a metal scraper can easily remove the old layers. Let it cool, and then season like this

Scrub your pan clean, wipe on a decent layer of oil over the cooking surfaces with a paper towel, place pan on stove top on hottest element, and heat until oil just stops smoking, remove from heat

If you keep it on the heat you will break down the oil polymer layer, and have to start again

This should take only a few minutes, not hours

Hmm..Normal? well it happens to me regularly as well, but I'm not sure I am good standard for 'normal'. What I always do is after cleaning my cast iron (by de-glazing as discussed here: Can deglazing a cast iron skillet remove the seasoning?) is to rub down the pan with a light coat of olive oil and then return that pan to the now cooling element on the stove. I doubt this is the same as the layers of hydrocarbons that are normally thought of as 'seasoning' but I never have a problem with food sticking to my cast iron.

For starters, I think this very normal. My pans also start looking like "bare cast iron" in the middle when I heat them up really hot. They will smoke too if I had any oil on them from previous use.

It has never been a problem however. I just do a quick seasoning of oil on that piping hot pan, give it a minute to smoke down & set in & it's ready to go. Not a problem with food sticking or anything... Not even eggs or fish.

I have tried (repeated times) Sheryl Cantor's Flax Seed Oil seasoning method - Fail. The oil is a "dry oil" alright. So dry, it ends up flaking off almost immediately. And, I have tried so, so many methods and different types of fats/oils without any miraculous success. I stopped worrying about it and just heated it up on my stove, seasoned it off for a minute and cooked with it. That has been the best method so far.

I'm beginning to think it is really the heat over time that seasons the pan and not so much the oil.

Being OCD and learning and trying every oil fat combo, you can think of and then some. Bacon fat, Crisco, butter, olive oil, flax seed oil, coconut oil, my preference is either bacon fat, butter, or Crisco with bees wax or trademarked crisbee. I can think of over the last two months. I stripped my lodge in my pizza oven at 800 on down, orbital sanded the inside of it with 80 grit and worked my way up to 600 grit. Every morning after use I wipe out if nothing stuck to pan flip pan upside down on stove and bake fat in thin layers after every use. Wife wants to kill me every morning for smoking out the house. In pizza oven or fire i bake in at 650 and wipe in new very thin layer every 5 minutes. The pan in so slick with such good season I can flip eggs with no spatula and a t small pat of butter. What newbies don't realize is its more about heat control. Just after the smoke point is where the season carbonized polymerization and it bakes in to a matte black finish. Go any longer then 5 minutes or higher heat beyond 600 you'll cook the season off. When you wipe out and see black. That's your seasoning. It will smooth out but you have to keep adding thin layers every time. Currently baking a new lodge pan to re-season at 850. Going to angle grind from 40 grit to 600 and re-season. 20 bucks some patience and diligence it will outperform any Griswold or Volrath or Wagner.