Mainly because your connection to the source seems to be a metaphysical connection. This is probably why "risking burning out" has more to do with loosing your control of the flows of the Source rather than automatically hitting some invisible number and destroying yourself. Many of the most powerful channelers we know of that died in apocalyptic ways, such as Lews Therin or Queen Eldrene, didn't instantly blow up, but had time to formulate complicated weaves and feats before they lost control.

In truth, I think burning out is more similar to what happened when Elayne started to unravel her own weave. You may need to bear with me here, as no one else I recall has proposed this, but you may remember that Aviendha explained to Elayne that the danger of unravelling your own flows had to do with the inability to control what shape the matrix fell into if you lost control - thus you could have a harmless flash of light or a cataclysmic explosion. You may also remember that saidar was badly affected, and was weakened in certain areas, and all we knew was that saidar itself wasn't damaged, but it seemed strained to the female channelers in certain areas. What I think happens is that if you lose control of the amount of Power you are drawing through yourself, your connection may become displaced, instead of the other possible outcomes, such as an unintended effect resulting from this loss of control or death. It would be similar to someone who lost part of their soul (which we know channeling to be connected to), which may be why burnt out channelers resemble someone else we know of...Birgitte. She too was quickly weakening, albeit in a different way, and needed a source of vitality in this world as well as something else to live for in order to survive. I would say that being burnt out is like being paralyzed, which may be why Nynaeve described Restoring a connection to the Source the way she did - she was looking for a physical ailment in Logain, and she was shocked when she bridged a gap or disconnection and realized that the Source now flowed into him as before. I think Severing is far easier to Restore, because you know exactly where the disconnection was afflicted, being in a localized area of the being it happened to, whereas being burnt out might entail returning to the location it happened or etc.