Magento – How Update on Save Indexing Works

If you only want to update a single product attribute without running the indexer, use the following method. It will be possible to update a couple of hundred products per second that way.

First, add a new product attribute estimated_time_of_arrival.
The, in your update script:

$product->addAttributeUpdate(
    'estimated_time_of_arrival',
    $date,
    $storeId // numeric store id value, e.g. Mage::app()->getStore()->getId()
);

If it's a global scope attribute, the $storeId doesn't even matter.
If you don't care about the store ID scope, you can also use:

$product->setData('estimated_time_of_arrival', $date)
    ->getResource()
    ->saveAttribute($product, 'estimated_time_of_arrival');

Both methods are equivalent (the latter will use $product->getStoreId()if the attribute has a website or store view scope).

Of course, if you use that attribute in some way that requires indexing, you will have to reindex after the updates.

Try indexing from the command line / ssh. Your VPS should have that functionality.

Execute the following from your /magento_installation/shell

Verifying the status if the indexes:

php indexer.php --status

To reindex the problem index, in your case the Product Flat Data

php indexer.php --reindex catalog_product_flat

Additional information: How to process Magento indexes from the command line

If an error presents itself at that time, there may be a problem with your mysql configuration or with the database itself. Feel free to post the relevant information.

UPDATE BASED ON NEW INFORMATION

I ran into this exact problem last year. You need to create a backup of your database and access via phpmyadmin.

I ended up dropping the table(s) (or you can TRUNCATE them).

catalog_product_flat_1
catalog_product_flat_2 

Then use the indexer.php to reindex.

You can reach more about this here