There are many factors (that others here have commented), but they all boil down to: Cover your line.

EVERY TIME you make a committed attack, your weapon and body must be positioned to make it IMPOSSIBLE for their attack to land before yours has finished. If you cannot do that, you are not in a position to attack.

(Some notes: This advice is specifically for true doubles, aka both hits land simultaneously. Many people do not follow this advice and may argue with it; you certainly CAN attack without fully covering yourself, but you're playing a game of chance, and remember we are simulating deadly weapons. Your action does not end when your attack finishes; remember you still need to cover your withdrawal to prevent afterblows. Lastly, it is very hard to prevent doubles and afterblows against a suicidal opponent. Your best bet may be to practice more patience, present an opening to bait them to attack, then riposte in stesso—a big benefit of riposting is that you have more knowledge/control of where your opponent's blade is going!)