Well there is nothing like giving up without even trying is there?but its not like you can shoot .22lr much further than 100m anyway...
The reason you "can't" shoot much beyond 100m is because you have a cheapo rifle.
With a decent rifle 200 yd shooting is well within the bounds of reasonable marksmanship. We routinely kill gophers at 150-170 yds or so and when the stars align, get the odd one at 200+ yds. Additionally a very accurate rifle allows much more fun at closer ranges. Inside 100yds we generally go for headshots.