Problem with serial.print(F("A lot of times anything"))

Try looking at calls to freeMemory() in loop() to see if you're hitting its max:

int freeMemory() {
  int free_memory;

  if ((int)__brkval == 0) {
    free_memory = ((int)&free_memory) - ((int)&__heap_start);
  } else {
    free_memory = ((int)&free_memory) - ((int)__brkval);
    free_memory += freeListSize();
  }
  return free_memory;
}