I thought your description of the IE 'right click' issue was very clear (probably more so to those hardened web users that spend hours with IE open.
It has been a common problem off all versions of IE and Microsoft are aware of it and have not released a fix for it (not free anyway).
As you say when you close IE it still remains. Regardless to your actions, the only time the right click returns is when IE is hard closed in task manager.
You will notice, when IE right click stops working, it returns temporarily, then after a little further browsing stops again.
You may have also noticed, when it has stopped working, and you close a tab or a window (if you have several open), it gives you back half the right click menu with a few options.
It is REALLLLLY ANNNNNOYING..
As you say, other browsers don't do it, so unless more people complain about it, microsoft chose to ignore it..
Apple are just as guilty for this with the shockingly poor battery life for the iPhone 4. Again unless enough complain, nothings going to be done about it.
For example, even on charge all night and morning, my new iphone 4 will die before bedtime, even with minimum system resources running, i have had 7 new ones, all the same fault, compared to a 3 year old iphone 3 that lasts 3-4days without a charge. With iPhone 5 due this year and increases in features the one thing apple need pushing on aside of the signal issue (Steve Jobs fix, don't hold the fone like that.. idiot.) is the battery needs addressing foremost.
These big companies like governments turn a blind eye to issues, unless us the small man (and woman for politically correctness) take action. On our own we do not get heard and are overlooked, however, united we pack a bigger punch whether its voting power or buying power.
Look at petrol (gas for you americans), here in the UK nearly 80% is Tax, 20% is Fuel Companies, if BP/Esso (exxon for you americans), Shell can announce 600 billion profits om 20%, what the hell are the Government raking in from all the fingers in all the pies. You challenge the Price rises, they quickly point the finger at the Fuel Companies.
We should take a leaf out of the french (put the fuel up there and the truckers block the roads until they drop it back down.)
Basically, The More that complain, the more gets done..
Anyway, rant over, back to IE.
Some bright spark has not released a fix yet, running 'ccleaner' does not help and although 'free ram xp' helps with memory and utilities such as 'quick shut down' are handy, currentky as of date and time of this post the only way to 'FIX' it is hard closing, 'iexplorer.exe' in the task manager processes, then re-opening it.
Englishman, Tim Berners Lee gave us the Internet for FREE, shame Microsoft, Apple, Governments and Record Companies don't remember this when they try to Police us..
I welcome as no doubt You do too a fix for this frustrating issue, however it is an IE fault accross its platforms and a Microsoft Responsibility to FIX Free of Charge!
You don't buy a car, then realise the manufacturer forgot to finish the engine and wants another £5900 to complete it. It's their issue to resolve the problem and it's getting them to 'pul their finger out and do something about it. Unless enough complain (as back to the iphone4 issue) they will happily take our money and play ignorant to the issue..