Mark Manning, 54 and of Brighton Road, Lancing, was last seen on 19 April 2014. His family have said it was "out of character" for him to disappear.
Since then police have searched a lake in Worthing, but found nothing.
A 49-year-old man, who was arrested on Tuesday, has been released on bail until 25 June.
The first man, 38, was arrested on 6 May. He has been released on bail until the same date.
A second man has been arrested on suspicion of murdering a bomb disposal expert from West Sussex who has been missing for more than a year.