Hi Friend,
Forwarding mode is to decide how user traffic should flow. management traffic always go over PAPI therefore regardless whether the forward mode is tunnel or bridge or any other, when AP do not receive PAPI (UDP 8211) traffic from the controller, it will reboot, it will not stay up.
In case of RAP we have RAP operation modes Standard, Always,backup and persistent. if the mode is standard, RAP also will reboot if do not receive PAPI else if it is Always mode, it do not care about the PAPI it will be up ever.
Bottom line is, AP will reboot if it loose connection with the Controller where as a RAP can be up in case if the operation mode is Always.
Hope you got some clarity.
Please feel free for any further query on this.