Connection issues with Airport Express Base Station (VERY old version -- 2012, maybe older?)

Apple produced three models of the AirPort Express base station:

1. 802.11g, models A1084 & A1088. These were introduced in 2004 & discontinued in 2008.
2. "1st generation" 802.11n, model A1264. These physically look identical to the 802.11g models. These came out in 2008 & were discontinued in 2012. Appears from what you posted, this may be the one you currently have. If so, Apple considers these in the "Vintage" support category, and there is no repair option available for them.
3. "2nd generation" 802.1n, model A1392. These are a different design format from the previous two models and look more like a later version Apple TV ... except they are white. These came out in 2012 & discontinued in 2018.

Regardless of which model you actually have, most consumer-grade networking hardware have a typical useful life of 5-7 years. The fact that yours is still working (somewhat) is more of a rarity. However, you certainly can try to keep it "running."

As such, one option would be to perform a "factory default" reset on the base station. This will result in the station returning to its "out-of-the-box" configuration, and will require that you set it up again for your networking requirements ... but doing this reset tends to resolve issues with it.

To perform this type of reset:

1. Start with the base station disconnected from power.
2. While holding in the reset button, re-apply power to the base station.
3. Keep holding in the reset button until the status LED starts flashing rapidly, and then, let go of the button.

You're very welcome!