There’s a difference between not being food motivated and not having an appetite. The former is more about a rabbit’s demeanor and self-control, while the latter can be medically relevant. It is important to distinguish between the two.
If the rabbit is literally not eating, that is a medical emergency. Pain, severe stress, anxiety… nothing positive causes a rabbit to not eat, despite it being hungry. So if this is the case, I highly recommend taking your rabbit to a rabbit-experienced, exotic vet ASAP. You should typically find your rabbit grazing on hay throughout the day and motivated to eat pellets and veggies eventually throughout the day.
My hope is that your rabbit is eating, but you and the rescue noticed perhaps he’s not tempted every time a veggie leaf or new hay is presented — and that can be OK. Some instances where you want to maybe take some action, whether it be about yourself or the rabbit, is if you suspect the rabbit is not eating because it is afraid/stressed by a human’s presence or the general environment. It is not unusual for a rabbit to not feel comfortable eating when a big human is in the room, especially right by the food! We can be very scary to rabbits. In terms of environment, if the rabbit is stressed due to feeling insecure, it’s not going to lower its guard and eat food (remember eating food leaves a rabbit vulnerable, so it’s not going to do it if it feels unsafe/unwell).
The ideal is simply the rabbit only wants to eat when its hungry, which is, in my opinion, a more uncommon characteristic of some rabbits, but not unheard of. One of my rabbits is very food motivated, in that every time someone walks to the kitchen and opens the fridge, he follows us to see if we will feed him. This happens regardless of the time of day. My other rabbit though is not food motivated. If I try to feed her veggie plate an hour earlier than scheduled, she won’t eat it, and I suspect because she’s not in the mood. This is also the case for sugary things. Currently, she is taking a very sweet medication that she loves, but if I try to give it to her after she eats her veggies, she will have none of it. Again, I suspect because she has the thought “Nope, I’m good”, while my other rabbit is essentially a bottomless pit of wanting food.
Having a less food-motivated rabbit can be a bit harder, as you can’t really tempt them to go places or do things with food. If this is the case for your rescue, I recommend figuring out what schedule works for him and his appetite. It took me about a month to figure out what time to feed evening veggies for my Fable to eat. During that time, there were days she had no veggies, simply because I missed “the window” it seemed.
Another potential cause can be aversion to certain foods. My less-food motivated rabbit is also very weary of trying new things. She is like a child who only eats the mashed potatoes; never the peas. So it was also a learning curve to figure out how to present things and when to give up due to her perception of foods. For example, she will never eat wet veggies. They must be dry.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.