Существует ли функция pam API, которая возвращает максимальное количество неудачных попыток входа для данного имени службы?

Похоже, что нет и нужно реализовать получение этой информации самостоятельно:

#include <security/_pam_types.h>

#include <pwd.h>
#include <fcntl.h>
#include <unistd.h>
#include <memory.h>
#include <stdio.h> /* for printf only during testing stage. */

#include <sys/types.h>
#include <sys/stat.h>


#define DEFAULT_TALLY_LOGNAME "/var/log/tallylog"
#define SYSLOG printf

static int get_tally( const uid_t uid, const char* tallyfname, struct tallylog* tally )
{
   struct stat fileinfo ;
   int lstat_ret ;
   int tfile ;

   lstat_ret = lstat( tallyfname, &fileinfo ) ;
   if ( lstat_ret ) /* if error we will try to create an empty file */
   {
      tfile = open( tallyfname, O_APPEND | O_CREAT, S_IRUSR | S_IWUSR ) ;
      if ( tfile == -1 )
      {
         SYSLOG( "Couldn't create %s", tallyfname ) ;
         return PAM_AUTH_ERR ;
      }
   }
   else
   {
      /* If the file is world writable or is not a normal file, return error */
      if (( fileinfo.st_mode & S_IWOTH ) || !S_ISREG( fileinfo.st_mode ))
      {
         SYSLOG( "%s is either world writable or not a normal file", tallyfname ) ;
         return PAM_AUTH_ERR ;
      }

      if (( tfile = open( tallyfname, O_RDWR )) == -1 )
      {
         SYSLOG( "Error opening %s for update", tallyfname ) ;
         return PAM_AUTH_ERR ;
      }
   }

   /* tfile is opened */
   int rv = PAM_SUCCESS ;

   if ( lseek( tfile, ( off_t )uid * ( off_t )sizeof( struct tallylog ), SEEK_SET ) == ( off_t )-1 )
   {
      SYSLOG( "lseek failed for %s", tallyfname ) ;
      rv = PAM_AUTH_ERR ;
   }
   else
   {
      const ssize_t rd = read( tfile, tally, sizeof( struct tallylog )) ;

      if ( rd != sizeof( struct tallylog ) && rd > 0 )
      {
         SYSLOG( "read failed for %s", tallyfname ) ;
         rv = PAM_AUTH_ERR ;
      }
   }

   /* closing tfile, and returning success or an error. */
   close( tfile ) ;
   return rv ;
}

int pam_tally( const char* username, struct tallylog* tally )
{
   if ( username == NULL || tally == NULL )
      return PAM_BUF_ERR ;
   else
   {
      struct passwd* pw ;

      memset( tally, 0, sizeof( *tally )) ;
      if (( pw = getpwnam( username )) == NULL )
         return PAM_USER_UNKNOWN ;
      else
         return get_tally( pw->pw_uid, DEFAULT_TALLY_LOGNAME, tally ) ;
   }
}

Вот содержимое заголовка, который содержит struct tallylog со всеми необходимыми комментариями. Я не публикую pam_tally.h, так как думаю, что все знают, что делать.

/*
 * Copyright 2006, Red Hat, Inc.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of Red Hat, Inc. nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY RED HAT, INC. AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL JULIE HAUGH OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

/*
 * tallylog.h - login failure data file format
 *
 * The new login failure file is not compatible with the old faillog(8) format
 * Each record in the file represents a separate UID and the file
 * is indexed in that fashion.
 */


#ifndef _TALLYLOG_H
#define _TALLYLOG_H

#include <stdint.h>

struct  tallylog {
    char        fail_line[52];  /* rhost or tty of last failure */
    uint16_t    reserved;   /* reserved for future use */
    uint16_t    fail_cnt;   /* failures since last success */
    uint64_t    fail_time;  /* time of last failure */
};
/* 64 bytes / entry */

#endif