How to Update multiple rows using $wpdb->update

It is a a bit of a stab in the dark, but I'm fairly confident that the problem is your foreach loop. It's broken (it will not execute anything because only an empty statement (;) is affected, and you will probably want it to have a block that contains the rest of the code.

As an example:

<?php
foreach(array(1, 2, 3) as $test);  
print $test . "\n";

will only print 3, while

<?php
foreach(array(1, 2, 3) as $test) // note the lack of the semicolon.
print $test . "\n";

will print a line for 1, 2 and 3. As a general rule, I recommend always being explicit with what you want to be repeated in a loop. Use curly braces, e.g.

<?php
foreach(array(1, 2, 3) as $test) {
    print $test . "\n";
}

It's easy to read and keeps you safe from these kind of bugs. If you have to add another line in the loop, just add it before the closing curly braces.

This code will probably be what you want.

$project_id = $_SESSION['project_id'];
global $wpdb;
$reward_ids = $wpdb->get_results("SELECT * FROM wpxa_rewards WHERE project_id = $project_id");
foreach($reward_ids as $reward_id) {
    $r_id = $reward_id->ID;

    $count = count( $project_reward_title );
    for ( $i = 0; $i < $count; $i++ ) {

        $wpdb->update( 'wpxa_rewards',

        array(

            'reward_title'       => $project_reward_title[$i],
            'reward_description' => $project_reward_description[$i],
            'reward_amount'      => $project_reward_amount[$i],
            'reward_shipping'    => $project_reward_shipping[$i],
            'est_date'           => $project_est_date[$i]

        ),

        array( 'ID' => $r_id ),

        array(

            '%s',
            '%s',
            '%d',
            '%s',
            '%s'

        ),

        array( '%d' )

        );

    }
}