So it seems that the first generation Apple Airports like mine overheat and cook their power conditioning circuitry.
So early last week I started noticing that my connection kept dropping. By Friday it was up for 5 seconds, restarting for 15, up for another 5 and so on. And now I've got red LEDs instead of amber and green.
Now I'm forced to use my only directly networked computer, a Mac 9600 running 8.6.
I am used to carrying my laptop around the house, noodling in front of the tv, the kitchen or the dining room. Alas, the desk I have the 9600 on is barely big enough to hold the monitor and a SCSI drive, so I can't easily use its network cable for the laptop.
Linksys is in my future.