Terminal drivers limit the length of input lines
As I noted in the comments, the trouble is almost certainly that your terminal driver won't allow you to enter lines that are longer than 1024 bytes; it won't allocate more storage. That applies in 'canonical' mode; see Canonical vs non-canonical terminal input for more information about that.
There's a simple test program (now in the question). When I run it on Mac OS X 10.11.4, I can enter 1023 characters plus newline, or 1024 characters but no newline until I delete one.
For the record, the input string was:
12345678901234567890123456789X123456789Y123456789Z123456789A123456789B123456789C123456789D123456789e123456789f123456789g123456789h123456789i123456789j123456789k123456789l123456789m123456789n123456789o123456789p123456789q123456789r123456789s123456789t123456789s123456789t123456789u123456789v123456789w123456789x123456789y123456789z123456789a123456789b123456789c123456789d123456789e123456789f123456789g123456789h123456789i123456789j123456789k123456789l123456789m123456789n123456789o123456789p123456789q123456789r123456789s123456789t123456789u123456789v123456789w123456789x123456789y123456789z123456789a123456789b123456789c123456789d123456789e123456789f123456789g123456789h123456789i123456789j123456789k123456789l123456789m123456789n123456789o123456789p123456789q123456789r123456789s123456789t123456789u123456789v123456789w123456789x123456789y123456789z123456789a123456789b123456789c123456789d123456789e123456789f123456789g123456789h123456789i123456789j123456789k123456789l123456789m123456789n123456789o123456789p123456789q123
If you copy and paste that with the newline, it will probably be entered OK. If you add any more characters, you will probably get the terminal beeping at you.
There's another question (fgets() is limited to 1024 bytes — what can I use instead?) that almost certainly ran into the same problem — and really wasn't given much in the way of useful help.
If you use a library such as the GNU readline library, it can put the terminal into non-canonical mode and then can handle longer lines because the terminal driver doesn't wait until the newline is entered before sending the data to the program. Rebuilding the kernel with a bigger limit on the terminal input line length is nominally an option on Linux-like systems, but not a task for the casual programmer.
Meaning of LINE_MAX and related macros
Also note that _SC_LINE_MAX is the sysconf() code for determining LINE_MAX, which must be at least the value of {POSIX2_LINE_MAX} (minimum 2048), which is documented as being:
Unless otherwise noted, the maximum length, in bytes, of the input line of a utility (either standard input or another file), when the utility is described as processing text files. The length includes room for the trailing <newline>.
Note that a terminal is not a text file. This limit says that utilities such as grep must not mishandle lines that are 2048 bytes long, but it might get confused by longer lines (for example, because it reads 2048-byte chunks of a line, and does 'beginning of line' matches at the start of the second or subsequent chunks of a long line).
The rationale for POSIX notes:
{LINE_MAX}
This is a global limit that affects all utilities, unless otherwise noted. The {MAX_CANON} value from the System Interfaces volume of POSIX.1-2008 may further limit input lines from terminals. The {LINE_MAX} value was the subject of much debate and is a compromise between those who wished to have unlimited lines and those who understood that many historical utilities were written with fixed buffers. Frequently, utility writers selected the UNIX system constant BUFSIZ to allocate these buffers; therefore, some utilities were limited to 512 bytes for I/O lines, while others achieved 4096 bytes or greater.
It should be noted that {LINE_MAX} applies only to input line length; there is no requirement in POSIX.1-2008 that limits the length of output lines. Utilities such as awk, sed, and paste could theoretically construct lines longer than any of the input lines they received, depending on the options used or the instructions from the application. They are not required to truncate their output to {LINE_MAX}. It is the responsibility of the application to deal with this. If the output of one of those utilities is to be piped into another of the standard utilities, line length restrictions will have to be considered; the fold utility, among others, could be used to ensure that only reasonable line lengths reach utilities or applications.
And the {MAX_CANON} referenced is described as:
{MAX_CANON}
Maximum number of bytes in a terminal canonical input line.
Minimum Acceptable Value: {_POSIX_MAX_CANON}
And elsewhere (<limits.h>), the minimum acceptable value for _POSIX_MAX_CANON is 255.
