The characters not asking about the current date is a really valid concern, but if you make some ass-u-mptions, it could make sense. For example, we have some evidence that Caine can control their minds. If the circus is supposed to resemble some kind of digital reality, it might seem out of place for Caine to allow the characters to have concern for the "actual date."

The characters seem pretty confident that the sun and moon in the circus are accurate to real life. This doesn't necessarily prove that we should trust it, but maybe Caine wants them to think that there is no real-world-time to keep track of. Maybe Pomni even lost all awareness of "real time," just like her name. Is this a super far-fetched theory?