Failed to update Linux headers on debian stretch / Debian 9

For

apt-get install linux-headers-$(uname -r)

to work, you need to be running a kernel which is still available from the distribution repositories; in most cases, this basically means you need to be running the latest supported kernel for your distribution.

On Debian, the simplest option is

apt-get update
apt-get install linux-image-amd64 linux-headers-amd64

(adjust to your architecture) to get the current kernel and matching headers, then reboot.

The linux-headers-4.9.0-3-amd64 is outdated , it is removed and replaced with the more recent package linux-headers-4.9.0-11-amd64 that's why you can't install it from the regular repository.

You can install the linux-headers-4.9.0-3-amd64 from the snapshot archive repository:

edit your sources list:

nano /etc/apt/sources.list.d/snapshot.list

Add the following lines:

deb http://snapshot.debian.org/archive/debian/20170609T034604Z stretch main
deb http://snapshot.debian.org/archive/debian/20170609T034604Z stretch-updates main
deb http://snapshot.debian.org/archive/debian-security/20170920T221221Z stretch/updates main

then:

apt -o Acquire::Check-Valid-Until=false update
apt install linux-headers-4.9.0-3-amd64

To access snapshots of suites using Valid-Until that are older than a dozen days, it is necessary to ignore the Valid-Until header within Release files, in order to prevent apt from disregarding snapshot entries ("Release file expired"). Use aptitude -o Acquire::Check-Valid-Until=false update or apt-get -o Acquire::Check-Valid-Until=false update for this purpose.