If you are running Firefox 4 or above, the browser disables 3rd party cookies by default. Please go to your Firefox Tools menu > Options (For Mac: Preferences) > Privacy > History > Firefox will: Use custom settings > select Always accept cookies options to enable 3rd party cookies for LastPass.com.
Another extension may be clearing cookies. Try disabling them and restarting the browser. If the issue no longer persists, reenable your extensions one by one to find the culprit.
Verify that your system clock is correct.
Are you behind a proxy or a firewall? If so, you may need to configure permissions for LastPass.
Try clearing the LastPass cache (LastPass Icon > More Options > Advanced > Clear Local Cache).
If you are using LastPass on a mobile device or tablet, ensure that the application data is stored in the device's internal memory and not on external storage, such as a MicroSD card.