A post-mortem examination yesterday failed to establish what caused the death of Peter Graham.
Mr Graham, 49, was found at about midday on 20 September, near his home in Port Ellen on Islay. He had suffered critical head wounds and was taken to the Royal Alexandra Hospital in Paisley, where he died on Wednesday.
Strathclyde Police said that although the tests were inconclusive detectives are continuing to treat the death as suspicious.
A force spokeswoman repeated appeals for anyone who saw Mr Graham between 17 and 20 September to come forward.
• Three men are being hunted after a member of a notorious crime family was fatally stabbed in a Glasgow flat.
Stephen McGovern, 37, was knifed after a disturbance at his home in Avonspark Street, Barmulloch, on Thursday night.
Police said the killing is not thought to be gang-related.