PayPal payment is stuck on Hold in BA, but is captured successfully on PayPal side. This occurs for all the customers of the reseller/provider.
PayPal is supposed to notify BA about successful/failed payment. It is to be done by the method
ProcessNotification. If you do not see such calls in the apache and billing logs, that means no notification is sent to BA by PayPal.
Check that Instant Payment Notification option is enabled, correct url to BA control panel is set, no firewall block sending requests from PayPal to BA.