Is there a strategy for endurance races?

The maximum amount of time you can have on your clock is 90 seconds. You gain additional seconds in two ways: passing cars and completing a lap. Passing a car nets you ten bonus seconds on your clock. Each race gives you a different amount of bonus time for completing a lap -- I've seen 10, 15, and 20 second bonuses given.

In any case, you must not just blindly race around the track, passing cars and completing laps as fast as you can. You must budget your time. If your current time is 85 seconds as you are about to pass a car, you should ease up on the gas and wait until it reaches 80 seconds. THEN pass the car, in order to net you the full bonus of ten seconds. Likewise, if you are about to complete a lap AND pass a car, you should slow down, complete the lap (thus getting the lap bonus), and once your clock dips below 80 seconds, THEN pass the car.

Playing in this fashion will allow you to obtain those high endurance times.

I'm with asylum on this. To avoid overtaking until the clock reaches 80 usually means (especially on the first couple of laps) braking hard because the cars on the first couple of laps are usually much slower than you. So you lose a lot of speed and once you do overtake you have to accelerate again. And if you don't get your timing right, you might not pass the car until the clock hits something like 75 seconds. So you may gain a few seconds extra at the expense of having to slow right down and lose momentum, something that will cost you those seconds.

Slowing down towards the end of a lap just get the most bonus seconds is equally pointless. Regardless of whether you slowed down or not, you will still start the new lap with 90 seconds on the clock. The only issue is whether or not slowing down means you have more cars to overtake. And surely this is an issue with how the game spawns new cars. But you still have to overtake those cars to get the bonus 10 seconds and by slowing down you've simply given yourself more distance to make up.

If you really have trouble with a single race, just disconnect and try the game offline, as the in-game AI cars are much slower than the online "time-shifted" ones. Note if you have already tried that particular race in the current playing session it will remember the downloaded racers, so leave the game and come back in and it should reset to the AI.

You could choose to play the whole game offline if you are really struggling, but note you will get no bonuses for time-trials this way, and you will have a nagging dissatisfaction at not truly completing the game!