One reason are the interest rate differences between the US and Taiwan: Right now, people can get more interest when exchanging their money to USD, so the demand for the USD is high resulting in a strong dollar. Also, if more people sell Taiwanese stocks than who buy (and subsequently convert their gains into USD), this puts further pressure on the NT$.
Forex markets are really difficult to predict accurately. If you want to minimize your risk, do cost averaging and do small, regular exchanges. Then you’ll at least get a good average rate.