It's not a matter of "IF" just a matter of "WHEN" your servo gears will strip, given enough time and use, every servo I have owned has worn the gears over time, usually you can feel slop starting to form before they actually strip, but in your case with a brand new servo it was a factor of having too fast of a servo unfortunately... yes many racers will swear that having a fast servo is worth the risk, but generally they are very clean drivers and will be less likely to strip a servo simply because they almost never wreck. For a sportsman level driver, I would start with a 0.12 sec/60° servo, then as your skills progress with fewer wrecks, then it may be worth considering a faster servo later, or simply keep your current servo as a backup for when your skills progress to having fewer wrecks down the road.
Which servo is right for me?

***UPDATE***
Not sure if this will help, maybe reducing the steering speed on your radio might yield the same effect, not sure how slow to get your 0.07 servo down to 0.12, but this "might" help reduce your chances of stripping gears.... just a guess assuming it's linear... 0.07 / 0.12 = 58% which is where I would set the steering speed to start out with.