Can i file an extension after my 1040 was rejected?

Sorry, an extension had to be filed on or before April 15, 2024.  There are no second extensions.  If you are receiving a tax refund then there are no penalties for filing after the due date.

I understand that when a return is rejected, there is a 5 day period to file. Given that, am I not able to file an extension?

unclear. it would seem if you filed an extension on 4/15 that was rejected you have 5 days to resubmit it. there is nothing about being able to file an extension after 4/15 if you did not submit a timely one that was rejected.  

if you live in Maine or Massachusetts you have until 4/17