How to make sure a fetcher is not called more than once at a time?

You could use the lock system to ensure the fetcher does only one API call at a time:

• Use lock_acquire() to create a lock. If it returns TRUE, then continue and make the API call. If it returns FALSE, then abort.
• After the API call is done or when an error occurs during this process, be sure to release the lock with lock_release(). It would be wise to wrap the API call in a try-catch block, so you can release the lock whenever an exception occurs.

The tricky part is ensuring that the aborted import can start at a later time. Maybe it's enough to just throw a FeedsLockException whenever fetching cannot happen. Else you may need to use Job Scheduler to schedule the import task at a later time. From FeedsSource::scheduleImport():

// Check for an existing job first.
$existing = JobScheduler::get('feeds_source_import')->check($job);
if (!$existing || $force) {
  // If there is no existing job, schedule a new job.
  JobScheduler::get('feeds_source_import')->set($job);
}

You can decide whether you want to check for locks in the implementation of the fetcher or at the start of an import, by implementing the hook hook_feeds_before_import().. There could be more than one fetch in a single import, but this depends on the implementation of the fetcher: the fetcher may report that fetching is not complete. See FeedsFileFetcher:

// Batch if this is a directory.
$state = $source->state(FEEDS_FETCH);
(...)
$state->progress($state->total, $state->total - count($state->files));