You can use combination of Parallel Block, Wait for field change and your other actions for sending email before 60 mins.
In your workflow settings -> Start Options you should select to Start automatically when an item is created and changed as shown in screen print below.
You have to use Parallel Block and as you have mentioned you already know how to send email 90 mins before due date, so those actions will be part of one side of parallel actions and another side would be to kill workflow if DueDate is postponed. Please find the set of actions for killing workflow when DueDate is postponed as shown below. (Please read 90 mins in below screen print as 60 mins)
Since we have set start option to stat workflow when an item is changed, a new instance of workflow will watch for new due date and send email accordingly or kill it self if it is postponed again.
Please let me know if this is useful.