The greatest threat to the Dominican Republic comes from hurricanes. The Caribbean hurricane season lasts from June 1 to November 30. August and September usually experience the most hurricanes. However during the rest of the year the climate is pretty calm and very predictable. It tends to rain at night, so during the day everyone enjoys perfect weather.
This is the current hurricane situation near Punta Cana, Dominican Republic based on data from AccuWeather.com
This is the current hurricane situation in the whole of Caribeean based on data from WeatherUnderground.com
Meteorological office of the Dominican Republic is pretty good about warnings. However – especially during the Hurricane season – you might still want to keep checking US National Hurricane Center) which does a fantastic job at tracking any weather activity in the Carribean.