Apple issues security software update for 802.11n AirPort Base Station
Apple has issued a security update for the 802.11n AirPort Base Station and Time Capsule units, the first one in over a year and a half.

The update was issued on Thursday afternoon, with Apple saying that it "improves the security of your base station and is recommended for all Apple 802.11n Wi-Fi base stations including AirPort Express, AirPort Extreme and AirPort Time Capsule." As of yet, details of what has been rectified are not available.
The last security-centric AirPort update prior to Thursday's 7.8.1 for this model was version 7.7.9 in December 2017. Version 7.8 was only for the AirPort express, and added AirPlay 2 features in December 2018.
To install the firmware update, AirPort and Time Capsule users have to perform the update through the AirPort Utility in macOS. If an update is available, an Update button is presented, which will command the base station to continue with the installation.
In April 2018, Apple announced it had discontinued the long-running AirPort Wi-Fi router line, with existing online and in-store stock being the last remaining units it would sell. The news followed a year after reports Apple had broken up its AirPort devision, shuffling employees to other areas and projects in an apparent sign the product line was close to ending.
In January 2018, Apple started to sell the Linksys Velop Mesh Wi-Fi System online and in store, an apparent break in Apple's policy to only sell its own routers, and the first third-party router to be sold in its retail outlets.

The update was issued on Thursday afternoon, with Apple saying that it "improves the security of your base station and is recommended for all Apple 802.11n Wi-Fi base stations including AirPort Express, AirPort Extreme and AirPort Time Capsule." As of yet, details of what has been rectified are not available.
The last security-centric AirPort update prior to Thursday's 7.8.1 for this model was version 7.7.9 in December 2017. Version 7.8 was only for the AirPort express, and added AirPlay 2 features in December 2018.
To install the firmware update, AirPort and Time Capsule users have to perform the update through the AirPort Utility in macOS. If an update is available, an Update button is presented, which will command the base station to continue with the installation.
In April 2018, Apple announced it had discontinued the long-running AirPort Wi-Fi router line, with existing online and in-store stock being the last remaining units it would sell. The news followed a year after reports Apple had broken up its AirPort devision, shuffling employees to other areas and projects in an apparent sign the product line was close to ending.
In January 2018, Apple started to sell the Linksys Velop Mesh Wi-Fi System online and in store, an apparent break in Apple's policy to only sell its own routers, and the first third-party router to be sold in its retail outlets.
Comments
2) The AirPort Extreme I updated was a decade old! I think the iPod was still Apple's biggest seller. An AirPort Extreme design (not generation) that has been discontinued for 6 years. When I saw this article I happened to be over at the house of someone's house whom I gifted an old 3rd gen 802.11n earlier this year. I pulled it out of my tech closet and dusted it off after years of sitting idle because they were paying a monthly fee to their internet provider for a clunky router that wasn't any more useful than this decade old AirPort. How many companies are doing that? How many of these are even in use?
please see kB HT210090
https://support.apple.com/en-us/HT201519
I just finished three Time Capsules and three Airport Express units without issues.
Mojave updated no problem of course.
Apple’s documentation is a bit unclear regarding this old express. It lists two models of express which neither of which are this particular model. It lists the (now previous) firmware for the n express as 7.8 which was never released for this gen 1 model and the “original” express which didn’t have n and is left on 6.3. I thought I would highlight it since it isn’t spelled out in the article or in Apple’s own support doc and the info may be useful to folks who may still have this same model kicking around.
In my opinion this was by far the best designed express style router from Apple. It plugged into the wall with no power cable and was really compact. The status LED was big and easy to see. It is nice that a model that was originally released in 2008 is still getting updated. Apple really tries to keep devices in service for as long as possible. Like Soli said previously, incredible!!