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Intermittent problems are often a result of interference. Interference can be caused by other networks in the neighbourhood or from household electrical items.
You can download and install iStumbler to help you see which channels are used by neighbouring networks so that you can avoid them, but iStumbler will not see household items.
Refer to your router manual for instructions on changing your wifi channel.
I ran the iStumbler and there wasn't any potential interference shown. Today, I noticed that an old email address was shown on iTunes, so I adjusted that, and the problem repeated itself. I then changed a couple other settings on Apple TV and restarted the Mac Mini. For now, it's working. I'm not sure which "fix" caused it. Hopefully, it was just a temporary issue. If it repeats, I'll probably exchange the Apple TV for a new one...unless someone else has a Correct Answer.