Koi explore by nosing and mouthing their surroundings. A plant that keeps coming loose may be getting disturbed at its roots, even when the fish are not eating much of its foliage. Start by protecting the planting area rather than assuming the plants and koi cannot share a pond.
Make planting containers harder to disturb
Use a stable, appropriately sized pond planter and suitable aquatic planting media. A layer of clean, suitably sized stone over the media may help keep it in place, provided it does not bury the plant's crown or create a hazard for fish. Position containers where they cannot easily tip, and follow each plant's depth guidance. See How to Choose Pond Plants for Your Water Garden for plant-selection basics.
Feed thoughtfully, not excessively
Offer an appropriate koi diet according to the food label and the pond's conditions. Extra food is not a reliable way to stop nibbling, and leftovers can worsen water quality. If plants are repeatedly uprooted, check the stability of the planters as well as the feeding routine.
Look at the whole pond
As koi grow, crowding and competition can change how they use the pond. Watch their behavior, maintain suitable water quality, and reconsider the layout if a planting area is constantly disturbed. Plant damage has more than one possible cause, so observe before making major changes.
The practical goal is to give plants a secure place to grow while keeping fish care and water quality in balance. For the broader role of aquatic plants, read Why Are Plants Important in a Fish Pond?.