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That is an interesting idea that is not typically considered in the drake equation as far as I know. That could significantly reduce the chance of finding intelligent life elsewhere.
I think it is in the drake equation effectively, it factors into the length of time that the civilization might send and receive detectable signals - It doesn't say why the Civilisation might collapse, but the planet becoming uninhabitable is surely one reason. On wikipedia for Drake Equation the Carl Sagan specification of L is in terms of the "fraction of planetary lifetime".
I think a missing factor might be how directional transmission and receiving is, if we can't broadcast to and listen to the whole sky equally then we might have a 1/r-cubed type issue with the chances of both listening and transmitting with enough strength/energy at the same time.