Local residents say the Lansdowne Monument above Cherhill, near Calne, has suffered weather damage.
The 38m (125 ft) Grade II* listed obelisk was built in 1845.
The National Trust said damage was "less than expected" and no date had yet been set for its conservation, which will cost over Â£600,000, due to a backlog of projects.
Local resident, Ralph Scott, said the monument had been neglected and was "an eyesore" since protective hoarding and scaffolding was put up around it in 2009.
"I'm sure they [the National Trust] have got enough money in their kitty to do little job on this. It won't cost that much."
Other local people told the BBC they believed the monument's condition had got worse in the past few months.
The obelisk was last repaired in 1990, but the stone used was softer than that used originally, and it has already started to wear away.
A spokesman said the National Trust was "committed" to the monument's conservation, but due to "a large backlog of projects" and "limited funding available" a date had not yet been set for repairs to begin.
"The monument is being carefully monitored and the deterioration is actually less than expected probably because of the mild winters, since it is frost action which causes the greatest damage," the trust said.
The monument was commissioned by the Third Marquess of Lansdowne to commemorate his ancestor, Sir William Petty, and was designed by Sir Charles Barry, who also designed the Houses of Parliament.
Concerns have been raised that a notable landmark in Wiltshire has deteriorated over the winter.