it appears that the deal is back - https://www.ozbargain.com.au/node/614361
My new 1-month Trial membership was about to expire in 2 days, on 12 Dec. Using Amazon Android app, I just went to Cancel - clicked "Continue to cancel", then accepted offer to change plan to Annual. Then again went to cancel, clicked continue to cancel button, switched back to Monthly plan and my trial got reset with expiry on 9 January now ! It now says "29 days left in your trial".
There was no message to extend the trial for another 30 days or anything like that. It just happened without prior notification.
Update: according to xyzzyxyzzy, this "hack" could be used multiple times and extend your Trial up to at least 6 months !!
Update2: Do not change your Prime membership card details, as this may cancel Trial "extendibility" (read this comment) Update 3: read this comment
For the record, I used this method for 6 months until recently. I don't know if the trick is doing this 3~4 days before the trial ends, but I forgot about it this month right before the expiry date, and the annual plan switch didn't appear