Avoid proceed-to-checkout-button text refreshing to default text in WooCommerce cart page

Solution:

Instead of overriding proceed-to-checkout-button.php file, should use the following instead:

remove_action( 'woocommerce_proceed_to_checkout', 'woocommerce_button_proceed_to_checkout', 20 );
add_action( 'woocommerce_proceed_to_checkout', 'custom_button_proceed_to_checkout', 20 );
function custom_button_proceed_to_checkout() {
    echo '<a href="'.esc_url(wc_get_checkout_url()).'" class="checkout-button button alt wc-forward">' .
    __("Checkout", "woocommerce") . '</a>';
}

Code goes in functions.php file of your active child theme (or active theme). Tested and works on last WooCommerce version under Storefront theme.

Now as you have done a lot of customizations in your templates or may be you are using some plugin in cart page for customization, the problem can remains due to those customizations.