"That’s a lot of trouble being caused by a two-line function. C may be a small language, but it’s not a simple one."
I disagree. C is very simple. You need to know C is not suppoused to work the same on platform and I guess behaviour you have tested is not defined by standard. I think every good C programmer know when he have to be causious because behaviour may be platform dependent. In matter of fact you did as well. I guess case you've studdied is not common to be used in real code. If so, there is very easy solution:
#if ((char)CHAR_MAX) + 1 > ((char)CHAR_MAX)
/* some code here */
#else
/* some code here */
#endif
Every problem has a solution which is simple, elegant, and doesn't work. This is it.
Section 6.10.1, paragraph 4: "... For the purposes of this token conversion and evaluation, all signed integer types and all unsigned integer types act as if they have the same represenation as, respectively, the types intmax_t and uintmax_t..."
Inside preprocessor directives, your chars aren't chars any more.
Your "char" in a preprocessor directive is either a uintmax_t or an intmax_t. Either way, it's going to end up as #if 128 > 127 or #if 256 > 255 -- so the first case will always end up being included.
So the good solution is make a test that finds it out, for example in configuration script and set proper preprocessor constant and test that constant instead.