Question

I’ve been trying to loop through a list and writing it to a file, why is the following not working?

loop_through_list(List) :-
    member(Element, List),
    write(Element),
    write(' '),
    fail.   

write_list_to_file(Filename,List) :-
    tell(Filename),     % open file to be written 
    loop_through_list(List),
    told.               % flush buffer

Answer 1

First, why it fails :
You use fail to provoke backtracking, which can be a good technique, but not there. Because it will make your predicate false in the end, when member has ran out of solutions. Then, once loop_through_list is false, told isn’t reached and the writing isn’t made properly (when I test it, the file is created but nothing is written).
If you use :

loop_through_list([]).
loop_through_list([Head|Tail]) :-
    write(Head),
    write(' '),
    loop_through_list(Tail).

instead, it works.

But, even with this code working, you might want to use
open(Filename, write, Stream), write(Stream, Element) and close(Stream) instead of tell and told for the reasons explained in the link at the bottom of this answer.
For example :

loop_through_list(_File, []) :- !.
loop_through_list(File, [Head|Tail]) :-
    write(File, Head),
    write(File, ' '),
    loop_through_list(File, Tail).

write_list_to_file(Filename,List) :-
    open(Filename, write, File),
    loop_through_list(File, List),
    close(File).

or

loop_through_list(File, List) :-
    member(Element, List),
    write(File, Element),
    write(File, ' '),
    fail.

write_list_to_file(Filename,List) :-
    open(Filename, write, File),
    \+ loop_through_list(File, List),
    close(File).

using your code and joel76 trick.

See Prolog how to save file in an existing file
It covers the same matter.