Darn, this is the second time I answer this question, and I can't find the previous answer, I guess it will have to go in the FAQ.
Indeed you cannot re-use the twig object to parse an other document. Contrary to most other modules (XML::Parser, XML::LibXML...), the twig is both the parser _and_ the parsed document. You can re-use the object if you parse several documents sequentially, but you cannot re-use it within a parse. So in your case you have to create a new XML::Twig object.
The reason for this is simple: incompetence. Mine. I wasn't very familiar with OO when I started writing the module, back in 1998, and I completely missed the object factory construct. Sorry.