In the past few months, rabbits have been spotted hopping onto village plots, where they have been nibbling the efforts of the village's vegetable growers.
The secretary of Shoreham Allotments Association, Clare Fowler, said: "It's just been this year.
"If you haven't got any of the young shoots covered, there is a tendency for the rabbits to find them and eat them.
"I don't quite know what damage has been done. But I do know that one or two people have lost a few things."
She added, while many of the allotments' plants were covered with nets to protect them against birds and butterflies, it was much more difficult to keep rabbits away, as they can burrow beneath such protection.
Mrs Fowler said the plotholders tended to see one rabbit at a time, with her husband recently spotting a young-looking specimen sitting on the site.
She added that a similar issue had arisen several years ago with badgers. On that occasion, the animals had to be removed by specialists.
After looking into possible options for dealing with the problem, Mrs Fowler said: "I asked the parish council whether we could shoot them, because I couldn't think of anything else, but they weren't happy."
Shoreham Parish Council member John Keates said problems with wildlife such as rabbits and badgers were to be expected in the countryside.
He explained: "The parish council has been asked if they may be controlled and its under consideration.
"There are health and safety and all sorts of other issues. Clearly, you cannot have people firing shotguns.
"You could fence off the allotment, but it would be expensive so to do."
The parish council has advised the allotment association to seek advice on the issue.
A 2005 Government guide for best practice in controlling rabbits suggested that damage from the animals could be reduced by rabbit-proof fencing.
But it pointed out numbers might also be reduced by gassing, shooting, kill traps, live-capture traps and ferreting.
Before using such methods, though, the Government said an assessment should be made to determine whether there is sufficient need for such action.