Thank you for contacting Yubico Support. We're received a lot of reports from users having trouble with the NEO on the Galaxy S6. Samsung is using a different kind of NFC antenna in the S6 that is supposedly less susceptible to interference transmitting through metal, but also has less range/power. I had a long conversion with a user a couple days ago that reported (after some troubleshooting) that the NEO has to be removed from a keychain (if it's currently on one) and held directly underneath the Samsung logo on the back of the phone. It really is a matter of proximity in this case. In the Galaxy line, we've had the best performance from the S4, with a bit more difficulty with the S3 and S5, and now the S6 appears to be the most challenging.
I find this site to be particularly useful when troubleshooting NFC issues, as it has images of the most popular Android phones and where their NFC antennas are located:
http://www.octopus.com.hk/customer-serv ... index.html