I'm not sure how common it is. (Sorry to profess ignorance, but I don't recall hearing it before).
When I Googled the phrase, I noticed almost all the links revolved around investing or finances. (Ah! No wonder a poor man like me hasn't heard it before...)
I thought this website explained it very well:
A falling knife security can rebound, or it can lose all of its value. As the phrase suggests, buying into a market with a lot of downward momentum can be quite dangerous. If timed perfectly, a buy at the bottom of a long downtrend can be rewarding - both financially and emotionally - but the risks run extremely high.
This site listed several investing cliches, including the falling knife expression, where it said:
"Never try and catch a falling knife. Wait for it to hit the ground then pick it up. The same applies to falling stocks."
A falling knife can land handle-side down (in which case it bounces), or blade-side down (in which case it sticks into the ground). If you're trying to catch the knife, and you catch the wrong end, you get hurt. Seems to be an apt metaphor.
The cliche is apparently well-used in investing circles. There's even a book with that title .
That said, I have no idea if its origins can be traced. It might just be one of those things that got uttered in the pit, and stuck.
Nice catch.
My first thought was, why not? Reinvention can be a good thing, if you make incremental improvements (in the world of clichés, I believe that's called building a better mousetrap).
I wondered if maybe the idiom could be used positively or negatively, depending on the surrounding words. For example, I'd consider the expression:
Don't reinvent the wheel.
to be negative, as you describe. However, the phrase:
...continues to reinvent the wheel.
might have positive connotations, suggesting perpetual improvements. So, I looked for some examples. I did find this one:
The artist continually reinvents the wheel — constantly striving for a sublime composition of balance, harmony and refinement.
but the vast majority of the findings were indeed negative:
The idea behind design patterns is to not continually reinvent the wheel.
Moreover, lack of interchange with other teams also often leads researchers to continually reinvent the wheel.
Clients don't want to pay for suppliers to continually reinvent the wheel.
The more I thought about it, the more I wondered if the writer didn't mean to say:
Eminem has continued to reinvent himself, putting his life on display, through a bevy of syllable-heavy, metaphor-driven cuts.
Reinvention of the wheel seems to be a bad thing – a waste of time – but reinvention of self seems to be associated with quests to remain relevant, or on top of your game.
I don't know if I'd go so far as to call your cited usage incorrect, but I don't think an editor's call to maybe strive for a more apt metaphor would be out of order.
Best Answer
It has the negative connotation that one is about to undergo surgery!
Since no surgery is completely without risk, and most is followed by a period of pain or discomfort, any expression describing it inherently contains a negative.
For that reason, we might euphemistically talk of "going into theatre"; a form of synecdoche, where the act of going into the place where surgery is performed stands for the whole process of going in there and having surgery performed. (We also use the same euphemism of the surgeons, theatre nurses, anesthesiologist, etc. who perform the surgery).
"Go under the knife" is a mild dysphemism, that doesn't add a negative connotation so much as focus on that which is already there.
This sort of bluntness can have a sort of euphemistic effect though, in a manner not unakin to gallows humour. Some people find it more comfortable to address the negative than to talk around it.
This sort of bluntness would require a degree of familiarity to be appropriate, and from that the ability to judge whether the person hearing it would indeed be the sort to prefer it.
It's also favoured as a dysphemism in more impersonal, informal writing. In journalism we'll find it used more of elective procedures, than for emergency or clearly required procedures, because "chose to go under the knife" both efficiently covers that a risk, and often a subsequent period of pain and discomfort, was entailed in that choice, as well as being a more vivid expression than the alternatives.