I don't know where you get the once a year success idea from.
Just screwing around, we've harvested several rabbits in one day with wrist rockets, using both glass marbles and rocks. (We like the glass marbles, you can go to a dollar store and get something like 500 of them for a buck. $5.00 ought to get you a lifetime's supply that can be easily cached, and no one's going to bother you for having them.)
And before you make a fuss over the use of marbles, notice I said AND ROCKS.
Taking small game with a slingshot isn't all that difficult, nor does it take a huge amount of time to find suitable rocks for use as ammo. Plus, with $5.00 you can cache (or carry) a bunch of ammo.
Why do you insist on making everything seem impossible?