Description:
------------
Essentially, it would appear that when creating a mysql connection, without persistence, each time you call the mysqli_connect() method it will clear the "last error" state value so calls to mysqli_connect_error() work correctly.

However, when you user presistent connections this doesn't work correctly. I suspect that the mysqli_connect() method is, when doing persistence, shortcutting the method and not clearing the state for what mysqli_connect_error() reads from. IE:

function mysqli_connect(...params) {
  if (host is persistent) {
    setup persistentHost
    return true
  }
  clearErrorState()
  doNormalConnectStuff()
}

As terrible psuedo code, I suspect that something like that is happening which causes the state to not reset until the next real connection happens (instead of pulling an existing connection from the pool).

Test script:
---------------
<?php

$mysql1 = '172.17.0.67';
$mysql2 = '172.17.0.69';

$conn = @mysqli_connect($mysql1, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql2, 'root', 'root', 'mysql', '3307'); // note: WRONG PORT
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql1, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql2, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$mysql1 = 'p:' . $mysql1;
$mysql2 = 'p:' . $mysql2;

$conn = @mysqli_connect($mysql1, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql2, 'root', 'root', 'mysql', '3307'); // note: WRONG PORT
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql1, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

$conn = @mysqli_connect($mysql2, 'root', 'root', 'mysql', '3306');
echo "Err?: " . ( $conn ? 'connected' : 'conn fail' ) . ' -- ' . mysqli_connect_errno() . ': ' . mysqli_connect_error() . "\n";

Expected result:
----------------
Err?: connected -- 0:
Err?: conn fail -- 2003: Can't connect to MySQL server on '172.17.0.69' (111)
Err?: connected -- 0:
Err?: connected -- 0:
Err?: connected -- 0:
Err?: conn fail -- 2003: Can't connect to MySQL server on '172.17.0.69' (111)
Err?: connected -- 0:
Err?: connected -- 0:

Actual result:
--------------
Err?: connected -- 0:
Err?: conn fail -- 2003: Can't connect to MySQL server on '172.17.0.69' (111)
Err?: connected -- 0:
Err?: connected -- 0:
Err?: connected -- 0:
Err?: conn fail -- 2003: Can't connect to MySQL server on '172.17.0.69' (111)
Err?: connected -- 2003: Can't connect to MySQL server on '172.17.0.69' (111)
Err?: connected -- 0: