...if regex...
   seek(LOG,0,0) || die "Seek error: $!";
   ...process line...
   truncate(LOG,tell(LOG))
[download]

Unless I'm missing something, you've moved the filehandle position to the beginning with seek. When you subsequently truncate to size tell(LOG) it truncates it to zero size, because 0 is where you've seeked to.

Try setting the position to a variable first:

   ...if regex...
   $pos = tell(LOG)
   seek(LOG,0,0) || die "Seek error: $!";
   ...process line...
   truncate(LOG,$pos)
[download]

That corrects the immediate problem, but will still leave the line in question in place. If you set a variable to the string length of the line you've matched, and

truncate(LOG,$pos-$stringlength);
[download]

that should get rid of your matched line.

Note: there may be better ways to do this.

Update: I also strongly agree with the first line of frodo72s response, especially as you've said that the file is growing quickly. I would be inclined to use two files, and write everything that doesn't match your regex out to the second file