It seems that only the 1st contribution in a recurring series is recorded in CiviCRM, and the others have to be noticed and entered manually. Is there any way that someone has found to fix this problem?
You need to set an IPN. Instructions are here. Basically, PayPal needs to send a payment notification (an IPN) to CiviCRM every time they process a payment, so that Civi knows to update the record. You need to tell PayPal what URL to send those IPNs to. In my experience, PayPal does NOT automatically find the IPN address - so find the exact path to
civicrm/extern/ipn.php in your path and supply THAT to PayPal for IPN. Also note that PayPal changes their interface all the time, so the place in the PayPal control panel where you enter the IPN URL might have moved.