Pledge payment link does not point to a publicly accessible page
This answer is for how to change the template issuing the email in question.  However, I don't know that the issue you're facing is due to the template.  See other answer.

The template for Pledge Payment Reminders is found in Communications or CiviMail's settings.

From the black menu bar:


  Administer > Communications > Message Templates


OR


  Administer > CiviMail > Message Templates


On the Message Templates screen, click on the tab at the top for "System Workflow Messages."  Scroll down and you should see an edit link for "Pledges - Payment Reminder."

On that edit screen, you can make any changes you need including changing the link.  Don't forget to make your changes in both the HTML Format and Plain-Text Format.

Before making your changes, I'd recommend copying and pasting the default template to a text document just to have it saved in case you need to revert back in the near future.