I can add a single object to a list with this code and query:
makelist(A, B, C, X) :- append([1, 2, 3],A, X).
?- makelist(a, b, c, X).
X = [1, 2, 3|a].
However rather than the usual separator comma (,) there's a vertical line separator (|) and I cannot add another object to the same list:
makelist(A, B, C, X) :- append([1, 2, 3],A, X), append(X,B, X).
?- makelist(a, b, c, X).
false.
There are several misunderstandings. First, lists and their elements are confused which leads to the "dotted pair" that is |a]. Then, it seems that the role of variables is not clear to you.
In the goal append([1,2,3],A,X) both A and X are supposed to be lists. However, you set A to a which is not a list. The problem behind is that append/3 accepts any term for the second argument. To see this, just look at its answers:
?- append([1,2,3],A,X).
X = [1,2,3|A].
So the A can be anything, but it should be rather only a list.
?- A = a, append([1,2,3],A,X).
A = a, X = [1,2,3|a].
Note that append/3 insists that the first argument is a list (or a partial list). Then once you have a bad list, you can no longer append it further. That is:
?- A = a, append([1,2,3],A,X), append(X, _, _).
false.
Note that I did not use your definition literally. Instead, I replaced certain arguments by _ since they cannot help.
The second problem stems from the goal append(X, B, X). This goal, can only be true if B = []. Let's try this out:
?- append(X, B, X).
X = [], B = []
; X = [_A], B = []
; X = [_A,_B], B = []
; X = [_A,_B,_C], B = []
; ... .
And:
?- B = [_|_], append(X, B, X).
loops.
While there are many answers for X, B is always [].