The banner next to the Lakeside Café on Waterloo Lake in Roundhay Park disappeared for the second time in as many months this week, and has been presumed stolen.
But instead of petty criminals being blamed, park conservationists have pointed the finger at campaigners, who believe swans are suffering malnutrition due to the banners.
Friends of Roundhay Park posted on their Facebook page about the assumed theft, writing: "Our 'Bread is Bad' banner on the Lakeside Cafe fence (which was put up in November to replace the one previously stolen).
"In non-flowing water like Waterloo Lake uneaten bread forms large rafts of rotting bread attracting rats and being a health hazard to canoeists and rowers.
"In your walks through the Park please look out for the stolen banners as the cost of the Friends replacing them diverts funds from more useful work in the Park."
The group has said they "can only assume" that "militant" swan welfare activists were responsible.
Many animal welfare activists argue that some swans and ducks suffer malnutrition due to the public being told not to feed them bread.
The Queen's chief swan maker David Barber claimed earlier this year that swans on the River Thames were being found "underweight" and even "wandering onto roads in search of food" as a result of campaigns against feeding them bread.
Advice from the charity Swan Lifeline says: "In common with advice from the RSPB and The Canals and Rivers Trust, Swan Lifeline does not recommend feeding 'human' foods to swans and other wildfowl.
"This includes bread, pizza bases, cakes, sandwiches which contain butter and meat products as they contain high levels of salt, sugar, fats and other additives.
"Bread and other human foods are not a substitute for a swan’s natural diet. Corn, chopped cabbage, spinach, peas and floating specialised swan and duck food pellets are the most suitable foods for the species."
John Ferguson, from Friends of Roundhay Park, said: "About three months ago the banner on the Lakeside Cafe fence was stolen. This was replaced with a new banner in late November. This second banner has now also been stolen.
"We can only assume militant activists from another group are responsible.
"Let's hope that most people have got the 'Bread is Bad' message by now. They certainly went through a lot of duck food we provide in the Lakeside Cafe."