The way the Paid Memberships Pro plugin hooks into the the_content and the_excerpt filters with a level of 5, you have two options...
1. Get the Paid Memberships Pro plugin developer to change how they protect the post and pages. (use a higher than default priority level for their content filters)
2. Add a define in your wp-config to tell PowerPress to use a different priority level when adding the player to the content.
Warning about option 2: The default priority level in WordPress is 10, and the Paid membership plugin uses level 5. They should be using a priority level of at least 11, assuming that all other plugins do not specify a priority level when they hook into the WordPress content. Basically, any plugin that adds content to the post will have a problem with this membership plugin until the priority level in the plugin is set to be higher. There may be a reason they did this though, that's why in option 1 above I said to ask the plugin developer to change the logic rather than just simply change the priority level of the hooks.
I will also warn that there are other plugins out there that use very high values for their priority levels. I would recommend to the Membership Pro plugin to do what we did with PowerPress and provide the option for a define in the wp-config.php to deal with such scenarios.
Other note, the way this membership plugin is designed, it is to protect your content on the web site. It protects the feeds but it uses the same wp-login sessions as the web site. This means you cannot use these feeds in any non-browser, podcasting apps will <u>NOT</u> be able to subscribe to the category feeds protected by this membership plugin. There may be an add-on plugin for this memberhsip plugin to make this work but I did not find anything with my quick search last night.