This is not unique to iDevices; but rather they often go to sleep so it is more noticeable. The timeout you are seeing is not DHCP related, but rather the timeout of the user in the active user table.
The setting is under Configuration --> Authentication --> Advanced --> User Idle Timeout (default is 300 seconds).
When this idle threshold is reached, the controller will send a probe request to see if the device is still there. If it is, the timer is reset. If it is not (ie. iPas asleep) then the user is dropped from the user table. Extending this too long however will keep disconnected users in the table for that time period as well.
If you have ClearPass you can manipulate this by pairing a guest with their mac address; and then doing mac authentication on the guest network; so when the iPad comes back online, it will pass mac authentication, rather than go to the Captive Portal page.