Bencic crashed out of the WTA International event as she was beaten 7-5 6-2 by German qualifier Antonia Lottner.
The Swiss was not the only seed to depart, either, with Carla Suarez Navarro throwing away a one-set lead to go down in three to Polona Hercog.
Pauline Parmentier is also out after losing in straight sets to Stefanie Vogele.
However, there was a win for Viktoria Kuzmova - now well placed to go all the way - over Giulia Gatto-Monticone, as well as for Rebecca Peterson and Vera Lapko against Magdalena Frech and Reka Luca Jani respectively.
Iga Swiatek, Fiona Ferro, Kristyna Pliskova, Evgeniya Rodina and Timea Bacsinszky all also advanced.