The group lost a resolution at the trust's AGM on Saturday to abandon the development on the estate of Erddig Hall in north Wales by 14,382 votes to 22,158. Votes for the development included more than 8,000 cast in a block by Sir William Proby, chair of the trust, on behalf of non-voting members.
A trust spokesman said: "The votes are given by people who trust the chair to make decisions in the best interests of the trust." He said Erddig needed repairs and was losing £300,000 a year.
One protester, Wrexham councillor Carrie Harper, said the trust had not explained why it couldn't fund Erddig out of its annual operating budget. She said: "This has gone beyond Erddig; it is about the ethics of the trust."
She criticised the block vote system and pointed out that without it the protesters would have been successful.