The GAC has occupied the 'eccentric' 480-seat theatre building, which is part of the Sussex University campus at Falmer, near Brighton, since it was built in 1969.
However due to a lack of funding - organisation bosses have admitted they needed £6 million to improve facilities - the centre has decided to call it a day. The last event is expected to be held in the venue next spring.
Doubts have now been raised about what happens next to the university-owned building.
A university spokeswoman admitted the exact role of the building is, at present, unclear although she confirmed that the building was not in bad condition and did not need a major cash injection.
She said: 'For the future, the university will seek to preserve the unique characteristics of this remarkable listed building, recognising that it offers social space, performance space and the largest tiered seating space on campus.
'A group is being set up to review the options available to the university for the use of the building.'