It would not be rabbits, marigolds are usually planted around a garden to deter them.
My best guess is a cutworm
"They love marigolds, tomatoes and all veggies plants. I usually find them sleeping inside my tomatoes. Very frustrating! They curl up if you handle them. They come out at night to feed and will eat your plant to the ground. They like to either sleep in the plant or in the dirt around the base of the plant. If you've got 1 you've got at least a few more!"
Look at these, first link is about them, second link is how to control them.
Something is eating my marigolds down to the stems, any suggestions on what it could be and how to get rid of?
It's bunnies. My mom had to run chicken wire around her flower beds. Looks lousy up close, but from the street, you can't see it.
Reply:Mom says "earwigs" and to spread some borax around the plant AND on the leaves.
Reply:Most likely it's deer.
It's easy to get rid of your marigolds, dig them up and throw them in the trash. Problem solved.
Reply:If its eating the leaves off and leaving the flowers, its earwigs.
If the whole stem and flower is gone, its probably deer. My rabbits don't eat marigolds. Fussy eaters, I guess.
Reply:Marigolds are the favourite food of the common garden snail and its cousin the slug.
Sprinkle crushed egg shells at the bottom of the plants, snails cannot cross the shells it absorbs their slime.
Or go out when it is dark with a torch and a bucket in which you have an inch of cooking salt. Pick the snails up and drop them into the salt. They disintegrate into a bubbly mass.
Try Snail and slug pellets if you do not have pets or small children.
Or put a large saucer of stale (or fresh) beer out. They are attracted to this liquid and drink themselves into a stupor and drown themselves.
Reply:If there's nothing but a nub of a stem, suspect rabbits. If it's the leaves being munched, do you see holes? Try jar lids full of beer (as beer traps) or Bug-geta pellets for killing slugs.