Submissions: They do not expire

How long are the clients submissions saved on jotform website?

The submissions do not expire. They will be stored until you either delete them, or cancel your account. 

However, your account can go into restore mode. That basically means your account is dormant. In this case your account will be disabled. It occurs when you don't log into JotForm for a few years. But your data will still persist. We can reactivate a dormant account on request.