MacAir drops network connection after five seconds.

Have you done a PRAM reset, CMD+Option+p+r...

Reset NVRAM on your Mac - Apple Support

In fact, do 3 in a row, takes a bit of time.

Intel-based Macs: Resetting the System Management Controller (SMC)...

Reset the SMC of your Mac - Apple Support

BJW45-__ Said:

"MacAir drops network connection after five seconds.: Two days ago, while I was on-line, I needed to take the Air back into the house. When I logged in again, I was unable to connect to my network.[...]"

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Troubleshooting Mac Wi-Fi:

A few thoughts to try...

I. Clear the Temporary Internet Files:

• Cookies perform remembrance of certain site-entered data.
• Cache keeps a snapshot of the last time you visited a site.
• Go Here: Clear your browsing history in Safari on Mac - Apple Support

II. Restart your Router:

1. Power: off the router
2. Wait: 30 seconds
3. Power: It back on

III. Boot in Safe Mode:

[Hold Down: shift key, upon boot], In Safe Mode, Login Items do not run at login, certain preferences are set aside, and damaged system files are then reset. So, once booted in to Safe Mode, wait 30 seconds, and then boot up normally, attempting another update install.

IV. Try a New Admin User:

What happens when you create a new administrator user, and log into it? Do you still get this error? If not, then it is likely an error with the current user. If so, then it is likely an error with your Mac.

BJW45-__ Said:

"MacAir drops network connection after five seconds.: [...]Lastly, when I boot up in Safe Mode, "WiFi: No Hardware Installed" shows under the icon when I hover over it with the mouse pointer."

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Reinstall the macOS:

If the hardware is not installed, then the drivers are likely corrupt, or have gone missing somehow. So, reinstall the macOS. Connecting to your router through ethernet may be the way to go about this. Use such a device like this, if no Ethernet port, and depending on the port you have:

• USB A: Apple USB Ethernet Adapter - Apple
• USB C: The Belkin USB-C to Gigabit Ethernet Adapter - Apple

About Reinstalling the macOS:

Another option would be to reinstall the macOS. Perhaps an install was not 100% successful? Sometimes, when major changes are made to your Mac(i.e. update installations), system settings (i.e. external devices) become manipulated, technically. So, when reinstalling, nothing would be deleted. It's just that items that have become corrupted or deleted, would be replaced or reinstalled back to where they should be. Go Here: How to Reinstall macOS from macOS Recovery - Apple Support. Important: Be certain you back up your Mac prior to the installation, as I mentioned in A2..