I don't think I ever completely *lose* senses, but I might experience a delay in processing sensory information when I'm already overloaded. For instance, there was one time at work when I found myself unable to make out what people were saying, and I was saying, "What? I can't hear you!" I also vaguely perceived a spike in my already high stress level. Suddenly, I figured out the reason why -- the fire alarm was going off, and had been going off for nearly a full minute. The fire alarm had been going off for close to 60 full seconds before I actually noticed.
I've had other similar experiences where my brain doesn't automatically process the information it's receiving, even as I'm already being affected by the stimuli.
ETA: There was no fire. The fire alarm was going off because someone had pulled the fire alarm.
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"And I find it kind of funny, I find it kind of sad./ The dreams in which I'm dying are the best I've ever had."