Audio randomly cuts out for remainder of clip - Adobe Premier Elements 11
I'm not that familiar with Premiere Elements, however in Premiere Pro, there is a conforming process during which a special preview video is made that can be used for more efficient editing.  I wonder if perhaps either the conforming has not finished yet or if perhaps you are having a problem with the conforming.  

Does it stop at roughly the same time on all clips?  Is the spot that it stops consistent?  How high is CPU usage and memory usage during the drop outs?

If the spot that it stops isn't consistent within a particular clip, then it is highly likely that it is an artifact of the conforming progressing.  If it is roughly the same spot across multiple clips, there may be some other kind of software or buffering issue going on that causes it to error or crash.  Also, if CPU or memory usage is high, it may support being a buffering issue where your system simply can't keep up with the playback.

This is also probably something that will be hard to troubleshoot over the Internet, so it might be worth contacting Adobe to see if they have any ideas as well.  It certainly doesn't sound like typical behavior.