Perhaps the damage is not from rabbits but an insect called a cutworm.
From the washingtonpost.com
Given a chance, nature will readily neutralize the cutworm threat.
From the newsobserver.com
That probably not the work of bunny rabbits but a plump, brown, soil-dwelling caterpillar called a cutworm.
From the washingtonpost.com
A few years ago, army cutworm moths were more prevalent.
From the kansas.com
To add insult to injury, a cutworm was crawling across one chickweed sample that Neier examined this week.
From the kansas.com
Use barriers such as netting or cutworm collars.
From the stltoday.com
It lives symbiotically, feeding off many species of grasses while providing the grass with protection from insects such as black cutworm.
From the sciencedaily.com
Many gardeners seem to think that the cutworm menace is a springtime problem because once the pests eat enough, they use the stored energy to mature into moths and fly away.
From the newsobserver.com
In Yellowstone National Park in the United States, the grizzly bear's diet consists mostly of whitebarkpine nuts, tubers, grasses, various rodents, army cutworm moths and scavenged carcasses.
From the en.wikipedia.org
More examples
North American moth whose larvae feed on young plant stems cutting them off at the ground
The term cutworm is used for the larvae of the Turnip moth (Agrotis segetum, Agrotis ipsilon, Agrotis exclamationis). Most cutworms are in the moth family Noctuidae, however, many noctuid larvae are not cutworms. Cutworms are notorious agricultural and garden pests. ...
(cutworms) Soil-living brownish caterpillars that feed at night, often severing stems of herbaceous plants.
A caterpillar of the moth family Noctuidae; particularly one which severs seedlings near the soil line at night
The larvae of several species of moths that pupate just beneath the surface of the soil. While in the larval stage they emerge at night and "cut down" seedlings, then devour them, leaving no evidence beyond the severed stem. ...