Next 20 years, barring a natural disaster in Europe, or the third world war, impossible. Argentina can't take the islands, and the famous C24
20-40 years, very unlikely, would require a collapse in the British economy while Argentina flourishes, and a willingness of the UN to accept an Argentine invasion.
40-60 Years. A peaceful transition to Argentine rule is possible, but again only in the case of a collapse in the British economy while Argentina flourishes. In that case the vast majority of the Falklanders will have been born after the war and MAY decide that the cost of paying for their defence isn't worth it. They could then negotiate a similar arrangement to what they have with the UK (full autonomy, but no need for massive defence costs).