timeout or blank page on page_archive.php when using get_posts with 2000 posts

I have created a page_archive.php template which will list all the posts and pages on my blog. It used to work fine, but I recently passed 2000 posts, and now the page is just blank. I think maybe it is timing out?

I can get the page to display properly if I limit the number of posts displayed to 1900 or less.

Is there something I can do to get all the posts to display on my archive page?

Here is the relevant code:

<?php $posts = get_posts( 'orderby=post_date&order=desc&numberposts=-1' ); ?>
			<ul>
				<?php foreach( $posts as $post ) { ?>
					<?php $title = '' == get_the_title( $post->ID ) ? get_the_time( get_option( 'date_format' ), $post->ID ) : get_the_title( $post->ID ); ?>
					<li style="padding-bottom: 0"><span class="the_date"><?php echo get_the_time( get_option( 'date_format' ), $post->ID ); ?></span>&nbsp;&mdash;&nbsp;<span class="the_title"><a href="<?php echo get_permalink( $post->ID ); ?>"><?php echo $title; ?></a></span></li>
					<?php } // end foreach ?>
			</ul>