Level 4 skier - still slips and falls at end of bunny slope

Have you checked the conditions on a info board (not those that gives your sim an option to go hiking and those where sims can get info on festivals). If it says icy conditions, it is normal for sims to constantly slip and fall even on bunny slopes.

You can also find out wether it's icy or not by either having your sim walk somewhere (as they'll usually slip) or by seeing if you can make snowangels (you cannot make snowangels in icy conditions).