I'm having the same problem with Autounlock as per previous posts but note that the questions and responses seem to refer to users running Safari 5.1 or Lion.
But I have the same problem with current software. My system comprises an iMac with OSX Snow Leopard 10.6.8 (fully up to date), Safari Version 5.0.5 (6533.21.1), and 1Password Version 3.6.1 (build 31057). Since my upgrade to 3.6.1, if I unlock 1Password, then I still have to unlock it again when I first use Safari (but only the once until 1Password locks or Safari is closed as per Khad's most recent reply).
I didn't have this problem with Safari 5.0.5 before I updated 1Password yesterday............ No problem if it's a known issue with this most recent upgrade and "production" versions of Safari, OSX, etc., but I wanted to check that I hadn't missed something (I've checked my preferences and they all seem to be in order.....).
Thanks in advance for any help, Mike