A couple of possibilities
- Go to your Apple menu and check that the location is set to Automatic: so >Location>Automatic. It can be set to other things - for instance, I have locations set for each of my clients where I need a fixed IP address. But for most people, it should be set to Automatic.
- Once you've checked that, do the stuff that Tony talks about.
We need to know whether anyone else can join your home network and experience the same problem. And it would be good to know exactly what happens.
I'm going to take a wild guess: go to >System Preferences…>Network.
Click on Advanced
Click on the tab DNS
In the pane DNS Servers there should be at least one TCP/IP address and it should be something like 192.168.0.1 or something of that ilk.
The DNS should be set to the same as your router address, but it might not be. In any case it should be in grey as it should be supplied by your router.
That's part one of the answer. The next response will describe how I have my home network set and it never goes down.
Let us know how you get on.