Michael Davies, 71, from Blaina, Blaenau Gwent, was staying at a hotel in Sandown with his wife Pat when he disappeared on 26 May.
His family thanked those who organised and took part in a search on Wednesday.
They said they wanted to join in, but it was difficult for them to return to the island from Wales.
In a statement released through Hampshire Constabulary, they said: "The whole family remains in limbo right now. Every day is a struggle as we feel unable to face things and move on."
A police spokesman thanked those who took part in the search, adding that detectives and specialist officers continue to work on the case.
There is no evidence to suggest Mr Davies has been the victim of a crime.
But there is concern that he may not have access to the blood pressure medication he needs.
The family of a south Wales man, missing on the Isle of Wight, have said they are "in limbo" and "unable to face things and move on".