Actually, a friend of mine who lives there told me the other day that it may reopen. This is what Wikipedia has to say:
The airport closed and ceased all operations on 23 December 2011. Since that time it has been mothballed with the aviation infrastructure and navigation aids retained pending an attempt by the leaseholder to change the use of the site in planning so that it can be disposed of for residential development.
As result of the announced closure a group from the Plymouth business community initiated a campaign to protect the airport site. The group known as Viable delivered a petition to the City Council with more than 38,000 signatures objecting to the Airport closure and asking the Council to protect the site.
A full Council debate on the petition concluded with a unanimous vote in support of the airport's retention. There were just two abstentions. Accordingly, in 2014 Plymouth City Council decided to safeguard the site for future general aviation use in the forthcoming Plymouth Plan on the basis of evidence provided in the report on which the Council had accepted the airport's closure.
Having achieved its campaign objectives, in 2015 Viable wound up its campaign and created FlyPlymouth Ltd with the objective of acquiring and reopening Plymouth airport. FlyPlymouth proposes to operate Plymouth Airport a general and business aviation airport not relying on commercial passenger services, the withdrawal of which led to the airport's closure.