In my personal experience, Meloxicam has either been prescribed as 1 dose per day or 2 doses per day, so my assumption from this is that it lasts several hours. That being said, based on the GI distress from the previous day and what you’ve reported, I personally find it unlikely that solely Meloxicam’s presence in your rabbit’s system would keep him from eating entirely (unless he has a reliable history of such an intense reaction from it). It is more likely that whatever GI distress is ongoing is also perpetuating lack of willingness to eat.

Re: whether to take your rabbit to the vet or wait it out, it’s a really difficult call for online users to make since we cannot be there monitoring your rabbit with you — if you can get an appointment with your usual rabbit-savvy vet, that could be considered the safe route. Whether going to a potentially non-rabbit-savvy emergency vet versus waiting it out is preferable is hard to say and will need to be your judgment. In general, if I’m seeing signs of the rabbit perking up, such as having energy, pooping, and peeing, I tend to wait it out a bit and do at-home measures: https://wabbitwiki.com/wiki/Gastrointestinal_stasis#At-home_treatment

How is your bun doing today?

I will look for the reference, but my memory is that meloxicam is metabolized in less than 12 hours in rabbits.  If the bun is feeling poorly, it shouldn’t make them not want to eat.

If your bun is still not back to normal today, I would contact a vet. There is also the consideration that it’s friday, so going into the weekend, which means it can be harder to get to a vet.

I’m glad you took him in, it sounds like he’s improved a bit. I would keep the vet posted on his symptoms though, they may want you to bring him back in for further treatment or the xrays. There are other ailments that can present like stasis (such as liver torsion).