Some store owners are experiencing a problem where PayPal is not sending the orders back to the store. The IPN is failing. As a troubleshooting step, get the latest version of the ext/modules/payment/paypal/paypal.com.crt file and replace the version on your store with it. See if things work after doing that.
The easiest way to get that file is to download the current version of Phoenix, either from the Products page or https://github.com/gburton/CE-Phoenix/archive/master.zip and extract the file from it.
I believe that file has been required for PayPal. So your store should have it. If for some reason you are trying to install PayPal on an older store, consider getting the PayPal App from the Marketplace: https://apps.oscommerce.com/fZMiN&paypal-app
The most recent version is older than the introduction of the file to Phoenix, so you may have to update the version of the file that comes with that. But the PayPal App version of the payment module does use that file.
Note that PayPal with IPN uses multiple files. There will always be one in includes/modules/payment plus it has files in includes/apps and ext/modules/payment/paypal . If you don't have all those files, then you may need to install the PayPal App to get them.