Apologies for the Duke of York* experience over the past few days.
The problem arose from a faulty SSL certificate. This is the code that tells your browser that the website is secure and trusted. There was only a minor error in the certificate – an incorrect date, I believe – but it was enough for Firefox to have a bit of a tantrum.
In trying to resolve this, last night I managed to lose the 'private key' needed to unlock the certificate, which is why the site suddenly appeared to be insecure for everyone, not just Firefox users.
A new certificate and key have now been issued, and everything seems to be back to normal.
* Duke of York – a term I have just coined to describe a website that is neither up nor down.