What's the minimum software for reliably live-streaming a conference?
The minimum software is hardware.  You want specialized hardware for doing top quality live streaming encoding reliably.  You could use something like the Black Magic ATEM television studio which includes 4 inputs and real time stream encoding capability to produce the conference really well or could use a cheaper stream encoder device that simply produces a direct stream.

You then need a CDN to handle distribution of the stream.  You can either use advertising supported options like Youtube or you can use commercial ones you pay for, such as UStream or any number of other services.  That's fairly independent of the streaming hardware you use.  Your end point just produces the stream, which just needs to be reliable and high quality, preferably specialized hardware.