OK Gphonei, I have now started up my TP-Link again and gone into the setup procedure. I checked, and there is no way to explicitly turn off WPA. I am offered three alternatives: Automatic, which lets the router decide, WPA, and WPA2, and in each of the last two I can configure the alternative chosen. I have to assume that by configuring WPA2, which I did before testing the Apple router, and did again now, I am disabling WPA, but I can't be sure. But the point is all my machines are using WPA2 to connect, so I cannot imagine that the router is going to try to connect back to just the Mac Mini using WPA. If it does, I'd say it's the Mac Mini which is sending an unclear request.
But once again, I am forced to ask the question, if all my other machines, an Asus, a HP, several iPhones and at least one iPad, running at least three different operating systems are in phase with the router and can connect, how can I say that they are all, including the router, incorrectly configured, and the only one correctly configured is the Mac Mini? That's like seeing 99 soldiers marching left-right-left and one marching right-left-right, and saying that he's the only one marching properly.
And I can't get away from the fact that, until October 2011, my Mac Mini marched left-right-left with all the other 99. Nor that, if I take my Mac Mini back to the state it was in a couple of years before October 2011 by installing Snow Leopard, it starts marching left-right-left again.
Whatever the fault is, it lies in the Mac, in fact in the operating system, in both Lion and Mountain Lion. For all I know, it might also lie in an updated Snow Leopard by now, but I've turned off updates.
Let's face it, I'm never going to get my Mac Mini with ML to work properly with anything other than an Apple router, and I have to decide whether to spend what it takes to buy one, keep my Mac Mini on Snow Leopard, or scrap the Mac Mini and go over to my linux box.
Another thing that worries me is your comment on the lack of arrows in the scroll bar (I have discovered btw that the up and down arrow keys do work quite satisfactorily in most circumstances). You said:
People with iMacs and Mac Minis can get an external touch pad to use as well. I, personally, use my three button mouse with the scroll wheel to scroll more than the arrows or litteral scroll bar.
What you are saying here is that, if I spend more money on Apple kit, I can buy a workaround to replace something with which there was no problem, but which Apple took away. It's the same problem as I'm having with wifi: if I spend money on more Apple kit, I can get my Mac Mini to connect again. Just phrasing the problem in that light annoys me so much that it prompts me to eliminate the first choice I mentioned above, and leaves me with reverting to Snow Leopard or migrating to linux.
It's a pity.
BTW, anybody got a pre-2011 copy of Lion they can upload to, say, Dropbox and give me access to? As I said before, I'd still like to test early Lion.