If you try to set a video mode with no resizable but the previous mode is resizable the the flag is not set. (Although the window behaves as expected.)

Here code that illustrates the problem:

/*
 * This program displays a deficiency in SDL.
 *
 * If the video mode was once set resizable it is impossible to set the mode
 * not to be resizable.
 *
 * compile: gcc `sdl-config --cflags --libs` resizable.c
 */

#include "SDL.h"
#include "stdio.h"
#include "assert.h"

void print_resizable() {
  SDL_Surface* screen = SDL_GetVideoSurface();
  assert(screen);
  if ((screen->flags & SDL_RESIZABLE) == 0) {
    printf("screen is not resizable\n");
  } else {
    printf("screen is resizable\n");
  }  
}

int main() {
  SDL_Init(SDL_INIT_VIDEO);
  
  SDL_SetVideoMode(800,600,0,0);
  print_resizable();
 
  SDL_Delay(10000);
  
  SDL_SetVideoMode(800,600,0,SDL_RESIZABLE);
  print_resizable();
 
  SDL_Delay(10000);
  
  SDL_SetVideoMode(800,600,0,0);
  print_resizable();  // this reports a error
  
  SDL_Delay(10000);
  
  SDL_Quit();
}