The jocular phrase had one but the wheel(s) came off is a meaningless statement made by a participant in a conversation as an admission of inattention or failure to understand what has just been said.

The earliest instance that I have found is from My Election Campaign, the satirical story of a fictional candidate in a legislative election, by Basil MacDonald Hastings, published in The Bystander (London, England) of Wednesday 22^nd October 1924:

We are, by the way, in need of money. […]
So, if you are inclined to help, give in cash if possible. If you are prepared to canvass, you will not be spurned; if you are willing to sweep out committee-rooms, you will not be insulted; if you will intercept eggs, broken glass and decayed vegetables at public meetings, you will be rewarded with a kind word; but if you bring cash, either in boxes, bags or sacks, you may be photographed alongside the candidate.
I have hesitated long about making this public appeal. “Isn’t it,” asked I of my Committee, “isn’t it infra dig?” The chairman, a humorist, said he once had one like that, but the wheel came off.

The second-earliest occurrence that I have found is from the title of a nonsensical story published in The Battle Creek Enquirer, and The Evening News (Battle Creek, Michigan, USA) of Friday 1^st April 1932:

Oh, Yes! He Had One Once but the Wheels Came Off
What’s That? You Don’t Understand What It’s All About? Oh, Well, Neither Does Anyone Else. It’s April Fool’s Day, You Know.
By Dale Harrison

New York, April 1.—(AP)—A nervous gentleman, carrying a gun on his back and leading a cook stove, strode through Grand Central terminal at 4:45 a.m. today, screaming:
“Stop that vandal! He’s running away with my 1926 telephone directory. It’s got a lot of good numbers in it.”
Suddenly he snatched from his vest pocket a lawnmower and hurled it at a lady from Juneau, Alaska, who up to that time had taken no part in the conversation.
Taking a fresh grip on the gun, the man passed on through the station and boarded the ferry for Weehawken.
It was Al Capone¹.

¹ Alphonse Capone (1899-1947) was an American gangster—cf. The first ‘public enemy number one’ was Al Capone.

The following is from the column Topics Of The Tropics, by Guy Butler, Sports Editor, published in the Miami Daily News (Miami, Florida, USA) of Sunday 26^th December 1943:

Flamingo Joe
Who is Flamingo Joe? This may sound like an excerpt from Ellery Queen² yet horsemen and visitors at Hialeah Park³ aver there is such a person whose impish antics are fast becoming legend.
[…]
Flamingo comes by his name through two distinguishing flamingo feathers worn sassy-like on each side of his hatband. He is the nemesis of Hialeah’s early morning sightseers and has come to be known as a self-appointed guide to the grounds.
[…]
The other morning Joe sized up a group of tourists holding a point of vantage on the clubhouse lawn. All present were visibly intoxicated with Hialeah’s magnificence. Our hero was going pretty good when one of the number, obviously a student editor of some high school publication, insisted upon breaking his continuity with the weirdest assortment of questions.
This serious-minded young lady had Flamingo Joe hanging on the fence for a time with her queries. A Hialeah gardener with a good ear and flare for newspaper reporting recorded the session for posterity so, if you are in the mood—
[…]
The Girl: I heard you tell a man you have the key to the quarter-pole, would you mind unlocking it and showing us about? I’ll bet it’s cute inside.
Joe: Sorry, lady, you’re just a little too late. I already loaned it to the Owl.
The Girl: What owl?
Joe: Oh, he’s just a fellow who spies on horses.
The Girl: Espionage on a race track . . . that’s incredible.
Joe: Yeah, I had one but the wheel came off.
The Girl: You had what?
Joe: One of those incredible things.
The Girl: You’re getting a bit difficult. Let’s go over to the stables […].
[&c.]

² Ellery Queen was the pseudonym of Frederic Dannay (Daniel Nathan – 1905-82) and Manfred Lee (Manford Lepofsky – 1905-71), American co-authors of detective novels featuring a detective also named Ellery Queen.
³ The Hialeah Park Race Track is a historic racetrack in Hialeah, Florida.

The title of the following article puns on the phrase—it is from the Liverpool Echo (Liverpool, Lancashire, England) of Saturday 17^th December 1966:

He had one, but a wheel came off . . .
A tanker driver’s back wheel was entered into the police lost property book at Preston yesterday.
Malcolm Platt, of 7 Fenderway, Pensby, was driving 2,000 gallons of high octane fuel along Blackpool Road, Preston, when he felt a shudder at the back of his tanker, stopped and found one of the double back wheels was missing, with the bolts sheared off.
The other half of the wheel was just hanging on.
Despite a search by the police and the driver, the wheel was still missing to-day.

Malcolm Grey used the phrase in his television column Pick of the night, in the Evening Chronicle (Newcastle upon Tyne, Northumberland, England) of Wednesday 2^nd December 1981:

Examples of aerotractology — I know, you had one, but the wheel came off — will be on show during the last in the current series of Collecting Now (BBC-2, 7.50).
It seems these are propaganda leaflets and during the last war millions of them were dropped out of the skies over this country and Germany. And it is not a forgotten art. Leaflet dropping is still going on today.

In her local-news column Garnered Here and There, in Public Opinion (Chambersburg, Pennsylvania) of Saturday 2^nd August 1952, Mary Garland mentioned the variant had one but the wheel fell off and said that the phrase was peculiar to the early 1930s:

Last week’s tractor-trailer mishap revived a saying of the early Thirties, “I had one but the wheel fell off.”

Al Palmer too wrote that the phrase was outdated in his column Ourtown, in The Gazette (Montreal, Quebec, Canada) of Tuesday 7^th September 1965:

Aging Process

You’re getting old if your vocabulary includes such snappy sayings as “so’s your Old Man,” “that’ll be the day,” “tell it to the Marines,” “I had one but the wheels came off” or “cheese it, the cops” . . .

Likewise, Alan Peterson wrote the following in his column Words, in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Saturday 4^th March 1995:

A common expression when I was a boy, we had one but the wheel came off, seems to have gone out of use. It was a jest when somebody used a word we did not understand.