This command spins through all your mailbox servers and reconnects all the uniquely identified but disconnected mailboxes in any one of the mailbox stores:

$Servers = Get-ExchangeServer
$Servers | `
  Where { $_.IsMailboxServer -Eq ‘$True’ } `
  | ForEach { Get-MailboxStatistics -Server $_.Name `
  | Where { $_.DisconnectDate -NotLike ” } `
  | ForEach { Connect-Mailbox -Identity `
    $_.DisplayName -Database $_.DatabaseName} }