This is a bad idea - explain to your client that it's against the principles of HTTP.
For example, a customer opens different pages of your site in two tabs/windows. The close the second one, and go back to the first tab, but not it's logged out and any link/page submit is going to cause an error. That would piss me right off.
Secondly, Andy's solution is only going to work if the customer has javascript enabled. This may or may not be an issue for you, but it's hardly secure.
Instead you should look at options like a short login timeout (e.g. 10-15 minutes if it's really sensitive data).