How to go about tracking down this error?

Can you post up your code?

The error is in the ESP8266 library, but that's probably not at fault - there's just so little memory available that it can't allocate memory when it needs it, and it crashes.

If you want to write to a file, I'd write it a bit at a time - each time you get new data, add it to the end. You might be able to use pipe...

There's an example of transmitting a file on the Internet page:

function onPageRequest(req, res) {
  var a = url.parse(req.url, true);
  var f = E.openFile(a.pathname, "r");
  if (f !== undefined) {
    res.writeHead(200, {'Content-Type': 'text/plain'});
    f.pipe(res); // streams the file to the HTTP response
  } else {
    res.writeHead(404, {'Content-Type': 'text/plain'});
    res.end("404: Page "+a.pathname+" not found");
  }
}
require("http").createServer(onPageRequest).listen(8080);

You might just be able to reverse that to:

function onPageRequest(req, res) {
  var a = url.parse(req.url, true);
  // ...
  var f = E.openFile(a.pathname, "w");
  req.pipe(f); // it should auto-close
}
require("http").createServer(onPageRequest).listen(8080);

but I haven't tried it...