VLC player does not remember last played position

The current, stable releases of VLC don't offer this. However, you can go to the VLC nightly build site to download the latest version of VLC 3, with an updated Yosemite interface and H.265 support. Most importantly for you, though, they have added resume support.

From http://nightlies.videolan.org, you just have to click on Mac OS X Intel, and then click on "last" in the list.

VLC nightlies have no support from the VideoLAN team, so you have to be careful. However, in my experience, VLC 3.0 has been pretty stable.

There is a plugin available called VLC srpos that will save and restore the playback position of the last played files. It is available here. There are numerous threads on this subject, I came across the plugin on the VLC forum, using a well-known search engine ;-)