Try connecting your computers with Cat5 cable and see if you experience the same problem.
If you don't, you're running into something messing with your wireless connection that happens periodically-like a neighbor using a ham radio that isn't properly shielded. Or maybe he's getting responses from Mars or something and they're what's messing you up!
If you DO have the same problem it's most likely that your cable folks are running network maintenance functions and the problem is at their end. The next step is to plug one computer into the modem (with a cable, not by AirPort, and power cycle the modem when you do this so it will accept the computer) and see if it happens THEN. If it does, then you need to call tech support and let them know what's going on.
Another thought: If your cable modem is dealing out a DHCP address, then it may be issuing them with a 24 hour lease time. The solution for that is to force the router to reconnect by turning it off for a few minutes. Do this at some point in the day when you're definately not using the machine, like 3 in the morning. This will establish the new lease at that time, and hopefully you'll never notice it again.
In some extreme cases, I've heard of people using those 24 hour timers you put lights on to fool the burglars into thinking you're home (yeah, right!) to power cycle their routers and/or modems at some hour they're never using the connection. It all depends on what's actually causing the problem whether you're going to have to go to those extremes.
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