Error checking fprintf when printing to stderr

According to the docs, fprintf can fail and will return a negative number on failure. There are clearly many situations where it would be useful to check this value.

However, I usually use fprintf to print error messages to stderr. My code will usually look something like this:

rc = foo();
if(rc) {
  fprintf(stderr, "An error occured\n");
  //Sometimes stuff will need to be cleaned up here
  return 1;
}

In these cases, is it still possible for fprintf to fail? If so, is there anything that can be done to display the error message somehow or is there is a more reliable alternative to fprintf?

If not, is there any need to check fprintf when it is used in this way?