Hogwarts drop outs and held back

Question

Based on another question, squib (and intuitively, muggles) won't be accepted into Hogwarts.

Admittance to Hogwarts is controlled by the Quill of Acceptance and the Book of Admittance. You name gets written in the book if you demonstrate signs of magical ability while you’re young, but this has to be your own magic: it’s not enough to ride off the coattails of your parents.

Squib have some background radiation magic around them that eventually wears off so they cat get in.

But what about the low aptitude students, students that fail to pass classes or graduate to the next grade. Do they get kicked out? Held back? Special school? Summer school?

(I'm american, not familiar with English boarding school practices either).

Answer 1

In short, yes. There are a number of mechanisms by which failing students can be "brought along", including holding them back an academic year. That being said, there don't appear to be any summer schools or special schools available to existing Hogwarts students.

Individual Professors may provide extra tuition

‘I’ll let you know in the usual way when the next one is,’ Harry said over and over again, ‘but I can’t do it tonight, I’ve got to go to – er – remedial Potions.’

‘You take remedial Potions?’ asked Zacharias Smith superciliously, having cornered Harry in the Entrance Hall after lunch. ‘Good Lord, you must be terrible. Snape doesn’t usually give extra lessons, does he?’ [emphasis mine].

_{^{Harry Potter and the Order of the Phoenix}}

Streaming

Student are streamed away from certain subjects if they lack capacity, whereas certain other subjects (notably Divination) are apparently open to all, presumably because the teachers need all the pupils they can get their hands on in order to justify their positions.

‘Well, that means I won’t see much of Professor Snape from now on,’ he said, ‘because he won’t let me carry on Potions unless I get “Outstanding” in my O.W.L., which I know I haven’t.’

_{^{Harry Potter and the Half-Blood Prince}}

Holding back

Students can be held back a year. This apparently happened to Marcus Flint (h/t to user Kattzar for reminding me).

Q. In the first book you said Slytherin house Quidditch captain was sixth year Marcus Flint. If there are only seven years of Hogwarts, why is he in the third book?

JKR. He had to do a year again! :-)

_{^{JKR Online chat transcript, Scholastic.com, 3 February 2000}}

and

Q. Why did Marcus Flint do an extra year at Hogwarts?

JKR. Either I made a mistake or he failed his exams and repeated a year. I think I prefer Marcus making the mistake.

_{^{J.K.Rowling Official Site - FAQ}}

Additional support (post-education)

There is also mention of Kwikspell correspondence courses, specifically aimed at those who've been through the education system (presumably at Hogwarts) and yet can't even manage basic spells.

Frankly, it seems most likely that students who show little or no capacity will simply not get very good (or any) grades in their O.W.L.S. and will generally enter the workforce in low-paid, low-skilled jobs.

Answer 2

It seems that one can be held back if they fail, Marcus Flint had to repeat his final year for failing the final exams. This was revealed on Rowling's site.