It would seem to me that the mouse only moves the cursor, it is not in charge of ige visibility and shape of the cursor.
Unless your problem is the cursor jumping to some random part of the screen making it difficult to find. That might be a mouse problem.
Otherwise I do not see how the mouse would make your cursor disappear.
Before spending any money, I would suggest digging up any old generic USB mouse, or borrow from a friend, just to see if the cursor disappears for that mouse. If it does, then it is not the mouse, and you are looking at a software issue.
When it comes to pointing devices, i personally I prefer the Magic Trackpad along with BetterTouchTool (free app) to add more gestures to its operations. Much better than a 2 button scroll wheel mouse "In My Opinion". Your mileage may vary.
I agree with Bob. A cursor disappearing likely has nothing to do with the mouse.
The cursor changes shape quite often as you scroll across a page, pointer, i-beam, hyperlink finger, etc. There is likely something interfering with the redraw when it changes shape. I've used Lion and Mountain Lion on three different Macs, and my daughters both have used Lion and Mountain Lion, and neither report any problems with the cursor disappearing. But, the only "mouse" I use predominantly is a Magic Trackpad. I do have a wireless Microsoft Mouse and Keyboard attached to a Mini, but I don't use the mouse on that. I had periodically attached cheap Dell and Microsoft corded mice to the laptops. No issues on any of them.
That other long thread you participated in had a lot of Adobe references, and someone thought they had it down to Java. Adobe, like Microsoft, likes to roll their own interface instead of using the built-in frameworks. If you use a lot of Adobe apps, it could be a conflict with Adobe's and some other program. If it was purely Adobe, there'd be a lot more people with that problem than the 30 to 40 on that thread.
The other "thread" in that discussion is the fact that many of them are using Adobe products, likely for digital design. That begs the question, "what other software is installed that most would use to assist the digital designer." Even if you are not a digital designer, you might have stumbled across the same piece of software.
My mouse cursor does often jump to a random part of the screen. When running InDesign, the cursor moving off-screen causes the whole documant to scroll to a blank part of the Pasteboad, so I loose my cursor position, and sometimes an object that was selected at the same time disappears off-Pasteboard.
For normal typing, the text cursor stops moving as I continue typing, so I lose text if I am not looking at the screen at the time. When the cursor stops, the contents of the window (at least I think it is the contents of the window rather than the window itself) moves slightly to the right and back again, then when the cursor re-appears it moves slightly again. This happens in all softwares: InDesign, Word, Safari web pages and (I think) in TextEdit. About every 30 minutes or so, sometimes longer. When I intalled M. Lion it was by the erase the HD and install method.
The mouse problem is not correllated with the charge level of its battery.
I will try again to use my Kingston optical mouse (it seems to use a generic Apple software). (I lacks many features of course.)
I also use the Trackpad in parallel to the magic mouse and it never gives any trouble like the above, although when I barely touch it it sometimes clears the Desktop (as with the three fingered spread gesture), or displays all windows unstacked (as with the three fingered upward gesture), or it zooms the screen.
I did not replace my Java as that long thread suggested for fear of messing things up.
In addition to using InDesign I use Photoshop.
I will investigate the wireless Microsoft Mouse.
I don't have any dodgy software on my Mac nor plugins, except Default Folder and SnapZPro, both reputable programs, as a precaution against glitches.
I have just thought of an interesting feature. When I erased and installed M. Lion, then the Adobe and Microsoft software, the pointer behaved OK for a time after the same glitches in Lion, the misbehaviour increasing in frequency after about three months.
It is disappointing that the Apple Genius bar was unable to solve this long-standing problem, even after doing tests overnight. I have taught myself to grin and bear it, and to fall somewht out of love with the Mac.
PS You will notice thatthis message has white on it!