If you reach this limit, your license will be invalidated.
How to move the installation of LiveAgent:
1. You can move all the files to the new location (or rename the directory where LiveAgent is installed).
If the database server changes with the domain too (e.g. moving installation to another server), you will need to dump the database of LiveAgent and import it into the new database on the new server.
Then, in accounts/settings.php of the installation of LiveAgent in the new location you will need to change the database connection information the new database server.
UPDATE `qu_la_contactwidget_attributes` SET `value`= REPLACE(`value`, 'OLD_DOMAIN_PATH', 'myOwnDomain.com/myLiveAgent');
UPDATE `qu_la_contactwidgets` SET `onlinecode`= REPLACE(`onlinecode`, 'OLD_DOMAIN_PATH', 'myOwnDomain.com/myLiveAgent');
UPDATE `qu_la_contactwidgets` SET `onlinecode_ieold`= REPLACE(`onlinecode_ieold`, 'OLD_DOMAIN_PATH', 'myOwnDomain.com/myLiveAgent');
UPDATE `qu_la_contacts` SET `avatar_url`= REPLACE(`avatar_url`, 'OLD_DOMAIN_PATH', 'myOwnDomain.com/myLiveAgent');
For the 'qu_g_settings' table:UPDATE `qu_g_settings`
SET `value`= REPLACE(`value`, 'OLD_DOMAIN_PATH', 'myOwnDomain.com/myLiveAgent');
As you can see on the examples above the syntax is pretty self explanatory and you can run similar queries on other tables in which you will find OLD_DOMAIN_PATH, for example if you added this URL to your email templates or to canned messages you might want to change it also there either manually from panel or by running similar SQL queries on tables where you find OLD_DOMAIN_PATH
On the other hand you will find OLD_DOMAIN_PATH also in some tables in which it doesn't really matter anymore like for example in qu_la_conversations, qu_la_message_groups, qu_la_messages and such. In these tables there is no point in changing the URL and moreover it can cause a lot of troubles if changed.
3. Now, when all is working again, you have to realize that your domain, or at least directory changed, so you have to replace the contact us buttons (chat buttons, forms) in your pages with the freshly regenerated ones that you may obtain in the agent panel.