If I'm able to resolve my issue I'll report it here. I'm reluctant to mess with the router's settings for fear losing the otherwise good performance I'm getting with the other devices. I suppose the best solution would be to buy a new router, try it out and if that doesn't improve anything or makes things worse, I still have the original set up to fall back on.
One of those other well functioning devices, btw, is the Denon RCD-N7 which is a receiver which connects with Apple devices via AirPlay, the dock/charger port or USB (all options are there) and allows control of those devices' menus through the Denon player. It also streams Internet radio and if you live in the US, I don't , it automatically connects with Napster and Last. FM. I'm a very happy customer.
Back to the Wifi issue, my router is a D-Link DSL 2040u. What is yours?