Well I've just bought an "Audax" frame second hand on Ebay - Dawes Giro 700 Audax. My definition of an audax bike (beyond what you need to comply with the regulations) would be it's whatever sort of bike works for the rider to get them over a long distance in the prescribed time.
I wanted something that filled the gap between my road bike and my tourering bike - infact when I measured out the geometries it was almost literally exactly inbetween. Wanted a balance of long distance comfort and stable handling yet still be light and fast and not feel like a heavy frame, wheelset and tyres are sapping my energy. The "relaxed" geometry should be coupled with a decent frame material - not just cheapo aluminium as the "relaxed" geometry of entry-level road bikes often have. The frame I've bought is Reynolds 531 Competition so the theory is that it should be light and stiff enough to get a good performance but good at soaking up the bumps and road buzz like steel is.
Audax events often specify you must have lights and mudguards so there should be the fittings for these. A lot of people fit a slightly wider tyre for comfort (25 or even 28c) so there needs to be clearance for those. A rack or something like a Carradice seems pretty common to carry extra clothing and enough food and supplies to keep you going for hundreds of km. A comfy brooks saddle or similar seems to be quite common, not often to be seen gracing a carbon mamil-special superbike!
There seems to be very little to choose from between what some manufacturers sell as "audax" bike and some as "winter" bikes (requirements for lights, wider tyres and guards being common). Infact when I was doing my research before I saw one on Ebay it seemed there's not a huge range and that the custom framebuilders seem to have a good chunk of the market.