AIR help as an application gets distributed to end users for installation on their PCs. You can then place updated .AIR files together with the XML file on a server. The locally installed help then checks that server folder. There is no publishing involved there.The field Output Location would normally be the within the SSL folder and you would copy the AIR file and the XML to the server location. At least that is the way I have interpretted it on the basis that all outputs get generated locally and only publishing goes to a server. I suppose you could try specifying the Output Location as the server and I will try that next time I am in the office. However, if your are having problems and are specifying the server, it would be worth changing that.
Web based AIR help gets published and that works OK for me.
I am not clear from you post what the problem is. If the above does not help, please clarify.
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For some reason I thought AIR files would be published to a set location like everything else, rather than having to be manually moved. I think previously my 'generating' folder was set as the network location, but I changed it to a local folder, not realising that the publishing step was only working for the browserbased stuff. seems a bit strange though that you can do it for the air file though.