I think I see what's happening...
I tried LAX->LAS one way, 12/21-12/22. If I'm logged in, I get several vehicle choices. If I log out and then try the same locations and dates. I get the message, "Error We’re sorry, but this location has no vehicles available during the selected dates and/or times. Please modify your dates and/or times or choose a different location."
Do you have Emerald Club membership? If not, you should sign up and see if that works. I have Executive Elite status, but I don't know if that really makes a difference.
Also, I know that some discount codes/account numbers and coupons can also result in the "no vehicles available" message. Are you using any specific codes or coupons?
One of the benefits of Executive Elite is a guaranteed vehicle. Perhaps this is the case in this instance, and LAX is otherwise sold out for one-way rentals out of the location.
-J.