Well most reptiles will get bored of the same thing over, and over, and end up refusing food for a long time if offered only one or two types. It also isn't exactly healthy you could say to have only the same food, and a variety even in our own diet should always be offered as well as theirs.
In the case of my tegu she will refuse the same food if it is given to her for more than a week, or even sometimes 4 days in to eating a sardine/salmon/turkey mix (just to use as an example) she'll straight up refuse it. However she's a picky brat and no where close to a bearded dragon.
She also refuses to eat crickets now because she got them quite a lot a long side her grounded up food. Only dubia roaches and hornworms now, luckily she gets those only occasionally or I'd be looking everywhere to find insects for her to eat if she got bored of those as well.
In the case of my beardies I have never had them exactly refuse the food they were eating as they always have a variety. Variety is key and should ALWAYS be offered.
In an insect feeding they usually have up to three kinds of insects, and in their salads they'll have about 2-3 types of greens and occasionally 3-4 types of fruits once or twice a week mixed in.
(They have refused food before, but I mean they haven't gotten bored of the food.)
Other than just refusing the same type of food, like I said it's not very healthy for them to only get a small amount of food items (both insects and greens/fruits). As insects are all different, some have a lot of
hydration, some have a lot of fat, some have a lot of protein, some have a lot of chitin like mealworms, some have high calcium contents and some have enzymes inside that are pretty good for the health of the animal eating them.
The same goes for all greens and fruits, each is different and not a single one is really a feed only type of food. By "feed only type of food" I mean you cant only eat this for food and you'll be fine as you'll end up lacking other nutrients that your body needs that other foods have more of.