Cookie written, but still requires login after every browser close.

I'm not sure what the problem is.

Settings:
Days to remember user: 30
Only listed pages require explicit login, no pages listed

Cookies:
After deleting all cookies from my site, I logged in (with "remember me" checked) and then logged back out. The cookies on my machine are:
PERSISTENT_LOGIN__ (expires in one month)
PHPSESSID (expires at end of session)

PHPInfo():
Here's a dump of the session portion of phpinfo for my site (php ver 5.1.2), in case that's helpful.

session
Session Support enabled
Registered save handlers files user sqlite
Registered serializer handlers php php_binary

Directive Local Value Master Value
session.auto_start Off Off
session.bug_compat_42 Off Off
session.bug_compat_warn On On
session.cache_expire 180 180
session.cache_limiter nocache nocache
session.cookie_domain no value no value
session.cookie_lifetime 0 0
session.cookie_path / /
session.cookie_secure Off Off
session.entropy_file no value no value
session.entropy_length 0 0
session.gc_divisor 1000 1000
session.gc_maxlifetime 1440 1440
session.gc_probability 1 1
session.hash_bits_per_character 5 5
session.hash_function 0 0
session.name PHPSESSID PHPSESSID
session.referer_check no value no value
session.save_handler user files
session.save_path /tmp /tmp
session.serialize_handler php php
session.use_cookies On On
session.use_only_cookies Off Off
session.use_trans_sid 0 0

Please advise if more info would be helpful. Thanks!