On the specific customer PayPal transactions always have the status "Failed".
In PAYPAL.log there is an error for these transactions:
Verification Response: INVALID
Verification requests to PayPal are not encoded. If there are '+','&' or other reserved characters in the request, they will not be escaped. The issue is considered as a bug, #PBA-51018, fixed in PBA 5.5.2.
Check the customer's name, e-mail address and other information for specific symbols like '+','&' etc., exclude such characters.
For permanent fix (without necessity to change the customer's details), update to PBA 5.5.2 or above. Since PBA 5.5.2 URL encoding is used for verification requests, so the requests are verified and payments are processed successfully.