When you attempt to "Save list as template", the "Include Content" check box is disabled.  This can happen for one of two reasons:

• The list content exceeds 10 MB
• The list ExcludeFromTemplate property is true.

A custom list template can be developed with the DontSaveInTemplate attribute configured and the value set to True.  The standard SharePoint Issues list is configured this way also.  To check a list and see if the ExcludeFromTemplate property is true:

$web = Get-SPWeb http://site_with_list
$list = $web.lists | Where-Object {$_.Title -eq "List Title"}
$list.ExcludeFromTemplate

The ExcludeFromTemplate property is read-only and cannot be changed.  Fortunately, you can use Central Administration to perform a granular backup of the list, and then use the PowerShell Import-SPWeb cmdlet to import the list with contents to the desired location.  Yay!