Is the problem to construct a $\mathcal{O}\mbox{*}(1.4^n)$ (or better) time algorithm for subset sum still open?
The way to tell if it is open is to read more recent papers to see if any of them make progress.  If not, it's still open.  The way to find more recent papers is to look up that paper on Google Scholar and look through all the papers that site it.  If someone has made progress, it's likely they'll cite that paper.

In general, don't expect to necessarily find a paper somewhere that says "it's still open".  People aren't necessarily going to bother repeating "yup, still open" every year.