I am facing the same problem once reported on this thread: https://lists.debian.org/debian-testing/2016/02/msg00000.html
However, I am running Debian Jessie on a Lenovo G40-70 with the most recent kernel: 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt20-1+deb8u4 (2016-02-29) x86_64 GNU/Linux
I have also tried different hibernation alternatives: either using GUIs (Mate, Xfce) or executing from the command line (issuing commands to the kernel). No success.
I have already managed to use hibernation when I was executing Ubuntu months ago on the same Laptop. Besides the OS, another setup difference is the HDD: Jessie is now running on a Samsung 850_EVO.