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.
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.