Are you using an ethernet cable or WiFi, if WiFi this can happen on some stock routers that come from your internet provider as they tend to not be very good. Destiny requires a stable connection. If using WiFi, try using an ethernet cable if you can or of using one already, try a power cycle of your router (turn it off for 5mins, then turn it back on and wait for it to boot up and try again to see if that helps)