PowerPress does correctly process the shortcode “powerpress”. The example <?php do_shortcode(‘[powerpress]’); ?> does work, as long as you are inside “the loop”. If you’re outside of the loop, or you’ve already made a call to the_content/the_excerpt(), then PowerPress will not re-add the player. You can force PowerPress to add a player using the same option for fixing poorly developed themes, go to PowerPress settings > Appearance tab and select the “Fix issues with theme” option.
To explain further, PowerPress only adds a player once to a post/page. PowerPress will not re-add a player for repeated calls to the_content (remember the_excerpt will call the_content and then strip out objects/flash). The way around that is to select the “fix issues with theme” option, which then aggressively adds the player to all calls to the_content filter.
The other solution to this problem is to directly use the the_powerpress_content() as you are now.
One other suggestion, wrap the call to the_powerpress_content() with a if function_exists check, this will prevent errors form displaying on your site if for some reason PowerPress were to be disabled, like during a plugin upgrade.
<?php if( function_exists('the_powerpress_content') ) the_powerpress_content(); ?>