Hi all,
Maybe this will help a little...
I seem to have a similar problem, I can only do the survey with a new token on the same computer if I delete the PHPSESSID cookie that gets created when I access the survey with the first token.
I keep reproducing it all the time despite changing settings in the survey. Currently, my settings are:
Allow saves? : No
Show [<< Prev] button : Yes
Participants may print answers? : No
List survey publicly: : No
Expires? : No
Expiry date : blank (but LS created "1980-01-01"

Use Cookies : No
Allow Public Registration : No
Anonymous answers? : No
Date stamp? : Yes
Save IP address? : Yes
Save referring URL? : Yes
Enable Token-based answers persistence? : No
... and it still doesn't work,

even after I close the window which should destroy the session...
My install:
LS: v1.71+
Server: XAMPP, currently testing locally
My computer:
Win XP / Firefox 3.01 => can easily visualise cookies as they are created.
The last PHPSESSID cookie shows:
Name: PHPSESSID
Content: 4b0356db09f23384f39ce8cb0207649a
Host: localhost
Path: /
Send for: Any type of connection
Expires: at end of session
I hope this helps!