Concorde isn't in any sense old. If this super-premium sector is uneconomic for the next few years, then just say you are going to mothball everything with a view to re-starting when things pick up. We know, even though that might be 10 years away, no-one is going to come up with another Mach 2 transport in the meantime.
They got the planes for free. I think they have a duty to pay for hangarage for a few years.
Maybe, however, the punters are leaking away to executive jets. They don't take much longer by the time you add the bits at each end and you can have proper meetings etc