Paypal Standard IPNs not being correctly handled leaving contributions as Pending (incomplete transaction)

Overview

My client recently reported that payment records in CiviCRM were not being automatically marked as paid/completed despite the fact that they were successfully completed and listed in the Paypal account. On investigating the issue it was clear that the IPNs were failing. I updated the CiviCRM install to 5.27.0 to see if this would resolve the issue. It didn't. Yesterday I updated again to 5.27.4. Still no change.

The issue appears identical to this case reported on Stackexchange: https://civicrm.stackexchange.com/questions/37277/paypal-standard-payments-are-being-accepted-but-marked-as-incomplete-transaction

I tried adding the patch referred to in Eileen's comment, but it looks like the effect of that has been to remove any information from the log pertaining to the IPN.

I've double checked the IPN URL provided to Paypal. If I point my browser to this URL I get the message:

Failure: Missing Parameter
module

The CMS is Wordpress 5.3.2