[masraum]

What Flipper/Brent said is correct, you should be able to look at logs on your router/modem.

Is there a PC that is wired to the router?

Is there a PC that is ALWAYS on and home?

I'm sure there are probably lots of ways to skin this cat, whether it be an app that's just for it or a ping scanner type of device or what.

It would be good if you had a PC that was wired to the router, that way you could monitor from that device (ruling out any wifi issues)

What's the signal strength where they usually surf from? Often certain parts of a house/office/building get crappier signal than others. How big is your place? One floor or two?