I think the opposite is true, the word has become less offensive over time.
In my experience, growing up in the London area in the 70’s, older people were more likely to be offended by the word.
I was told as a boy that “knackered” means “sexually exhausted”.
It is used more generally to mean tired out. If it really does have a sexual connotation, it seems most people are unaware of it.
As pointed out above, “knacker” in Ireland is a very offensive word for someone from the Travelling community, so people would be cautious of saying “knackered” for that reason.
I’d never heard the sexual connotation before reading this thread. It is hardly a common word in the Great Lakes region, so “knacker” was always the guy who hauled away dead livestock carcasses and “knackered” was always really tired, to the point of being worn out like an overused draught horse “on its last legs.”
(Even then, I doubt I have heard it much outside the circle of my in-laws among whom are many, many farriers and farmers.)
(I guess I could see it being used after a really exhausting bout of sexual activity, but I would have assumed the “tired/on my last legs” meaning without thinking that “knackered,” itself, carried a sexual connotation. Is it regional? Is it generational?)
I have never heard it in US English, but it’s quite common (in my experience) with UK English. I’ve never noted any rude or impolite connotation to it.
These days it’s only rude to people who consider ‘bum’ and ‘crap’ to be terribly rude words and think girls shouldn’t whistle, i.e. my Dad. I doubt you’d meet anyone under 50 who was offended by it.
“Bum” is considered extremely rude in the US. You’re supposed to call them “homeless”. 
I’ve never heard of the post sex meaning but my mum disliked the word, because it was vulgar I assumed. Supposedly the cockney rhyming slang is cream crackered but the only person I know who uses that is a Yorkshireman.
I too was taught it was “tired after sex” in the playground, but that meaning evaporated as I became an adult. I wonder if it’s just one of those kid ULs.
In Australia knackered means you were only fit for the knacker’s yard, worn out etc.
Knackers is also slang for your gonads.
Most people wouldn’t be offended but I wouldn’t use it in a business meeting.
I’ve only heard it in the dead horse context. And indeed I learned the word from James Herriot books when I was a kid.
Does anyone else get the sense it’s catching on here? I’ll bet in five years, everyone will be saying it.
Huh, never heard the sex-connotation before. I really like the word, it seems such a good description of being really tired. And I can use it in front of my upper-middle class gran with no problem.
Anyway, I always associated it with the knacker as well (and using a word that means “balls” for “tired after sex” doesn’t make sense to me). The whole thing rather smells of the “niggardly confusion”. I can imagine a word that is associated with common speech becomes suspect of actually being offensive.
Etymology online seems somewhat inconclusive, relating it to castration but locating its origins in the dead horse region. But I think I’d still call that a win for the dead-horse-camp.
As the original poster, just wanted to say thank you for all your responses. I can’t believe I never associated the word with ‘knacker’s yard’, which I have heard many times on British TV (if anyone remembers Steptoe and Son (remade in the US as Sanford and Son I believe) it was used almost every episode.
Just to push the question again though, does anyone have any idea of the origin of the actual word ‘knackered’? What I mean is, if it comes from the same source as ‘knacker’s yard’ where did they get ‘knacker’ from as well?
Thanks again everyone for your input, this is genuinely fascinating, and great to hear how people first heard or learnt the word.
My computer dictionary:
The Online Etymology Dictionary:
Edit: Saw after posting that gracer beat me to the Etymology Dictionary.
Knackers meaning testicles and knackered meaning tired have different roots.
Knack, a verb meaning to knock or to strike sounding blows goes back to the fifteenth century. From that sense we get knackers, a seventeenth-century term for a musical instrument like a pair of castanets, involving two hinged pieces of wood which are knocked together to produce a sound. And from the nineteenth century the word starts to get applied to a pair of testicles. You can see why.
Then we have knack, a noun meaning a trick or artifice, or an adroit or ingenious manner of accomplishing something. This sense survives in phrases like “he is forever breaking the rules, but he has the knack of avoiding detection”. From this we get another sense, a clever contrivance or modification to some object. This kind of knack may improve the utility of the object, or it may be ornamental. From this, it’s though, we get knacker, a saddler or harness-maker (sixteenth century), and from this we get knacker, one who buys worn-out horses, slaughters them and renders them down for glue and leather. And that gives us knacker, a verb, meaning to slaughter and boil down for glue, which gives us knackered, the feeling you have after you’ve been slaughtered and boiled down for glue.
The notion that knackered refers specifically to exhaustion through sexual excess probably comes from a comparatively recent conflation of the two words. Until comparatively recently everyone knew what a knacker did and what went on in a knacker’s yard, and it would not have occurred to them that knackered had any sexual connotation.
I grew up in Ireland in the 1960s and 70s and knackered was a colloquial, informal word for “tired”, with no sexual connotations. We were also familiar with knackers meaning testicles, but did not consider that there was a link. Knacker meaning an intinerant traveler was derogatory. It referred to the fact that travelers used to deal in (generally low-grade) horses.
I know THAT feeling
Old English playground joke from the 80’s:-
What’s the difference between a fit bird and an unsurfaced road?
One knackers your tyres, and the other tires your knackers.
NM
I think you’re probably on to something there. A bit like the African bum disease.
Slightly OT, but clearly related. Bollocks. I think the one time I have had a posting killed by a moderator on a list was when I used the word. Bollocks aka knakers, aka testicles, was considered rude. However for bollocks we have a very famous legal opinion that differs. The etymology of bollocks presented is rather interesting in its own right.