You may want to consider switching from K2 to something like else like EasyBlog then... Or just don't use K2. It seems like the default for K2 is to follow a workflow that conflicts with yours.
Otherwise you can modify K2 to suit your needs... I really don't recommend modifying extensions because then you can no longer make updates to them unless you plan to make the modifications every time you update (which is a pain).
You problem resides in the administrator/components/com_k2/models/item.php The following lines are form version 2.6.1 line 785.
if ($front)
{
if (!K2HelperPermissions::canPublishItem($row->catid) && $row->published)
{
$row->published = 0;
$mainframe->enqueueMessage(JText::_('K2_YOU_DONT_HAVE_THE_PERMISSION_TO_PUBLISH_ITEMS'), 'notice');
}
}
If I understand you correctly you want something more like:
if ($front)
{
$row->published = 1;
if (!K2HelperPermissions::canPublishItem($row->catid) && $row->published && $isNew)
{
$row->published = 0;
$mainframe->enqueueMessage(JText::_('K2_YOU_DONT_HAVE_THE_PERMISSION_TO_PUBLISH_ITEMS'), 'notice');
}
}
If I understand their model right by adding a check for $isNew to the if statement it will only apply published = 0 to new entries. Which, if I understand you, are the only ones you want to affect. This way if if the article already exists and it's published it will always stay published unless an admin changes it to unpublished.
I'm not sure if this will work the way I expect so let me know.