A320 ROLLOUT mode
 

When does ROLLOUT mode get disengaged automatically after landing in case of manual or automatic landing?

? Remains until AP is disconnected. Isn't a mode during a manual landing.

In my experience with ROLLOUT mode engaged you have to disconnect the A/P otherwise you cannot turn off the runway! Many a pilot new to Airbus will have discovered this out whilst trying to make the first high speed turnoff! It's mu understanding that this mode acts through the NWS.

It is a mode for both auto and manual landing.. Check next time when you land

Yes, that is right.. But disconnecting AP doesn't disengage the ROLLOUT mode.

I think it's a certain amount of heading discrepancy from the landing course which causes it to disengage. When you turn off the runway at a certain time the mode is dropped.
Compare with more conventional aircraft which retain it (or GS/LOC) until you disengage it (or switch off the flight directors).

Yes, I noticed that too recently. when you clear the rwy, at some point it disengages itself.

I am looking for a reference to such disengagement in the FCOM.. Any idea?

It's 25 degrees off the inbound course. I'll have a look for the FCOM ref when I have time.

Check out PRO-NOR-SRP-01-70 which says:

At the end of the Rollout:
Disconnect the autopilot.
If the flight crew does not disconnect the AP at the end of the rollout, and uses the nosewheel steering handwheel to taxi the aircraft off the runway, the following will occur:
The AP will try to steer the aircraft back to the runway centerline, if the nosewheel steering handwheel is released and the aircraft heading is less than 20 ° off the runway centerline.
The AP will automatically disconnect, if the aircraft heading is 20 ° or more off the runway centerline.