I have the exact same problem with my wordpress install.
https://www.esinner.com/
I have <?php the_time(‘F jS, Y’) ?> called within my templates, yet I only have the day and the year showing also. I have disabled the my_hacks.php inclusion and also removed the php call to that function in my template, this makes no difference though.
The only hack I use is the recent comments hack, though I will change to the plugin instead and see if that helps. Other than that, the the_time calls are placed in the wp loop and are structured the exact same way as in the default kubrick theme (which works), yet in my own theme the date doesn’t work. Go figure…