In general, just like any network device, it should just reconnect when the router reboots. 
 

Sometimes, when the power comes back in, there’s a surge in the power, which causes issues with more sensitive devices like the router. If your Arc doesn’t reconnect, I’d suggest unplugging all Sonos devices from power, then rebooting your router. Since at that point, there is no ‘surge’ of power, but a regular level, it should reboot fine, and reload all of the appropriate software that runs the router’s processes. Once the router has come back up, plug back in all Sonos devices. Because they were unplugged while the router was rebooted, they’ll both reload their own software, and request new IP addresses from the refreshed router, and you should be good to go. 

Thanks for the reply! 
I’m less concerned with total power outage than when I turn off the router and later restart. No loss of power to the Sonos, just loss of connection to the LAN and the Internet. 
i was able to get the Sonos to work after unplugging/replugging. I was hoping the Sonos would reconnect with the LAN and Internet automatically, but that didn’t happen. 

Normally, it should, unless something odd has changed on the router’s side, such as an SSID change, or a channel type change (no longer b/g). Pretty much like every other device in the network. 

Thanks, that’s what I thought.

I tried turning off my modem/router last night and restarting in the morning. The Sonos Arc connected fine to music, but getting TV sound was a challenge. I ended unplugging/replugging the Sonos power cable, then turning on the TV, which allowed the TV sound to work through Sonos. So the problem seems to be with reconnecting to the TV sound. I can leave the modem/router on all night and that should solve the problem.

As I understand things, your WiFi network should have zero impact on your ARC or eARC connection to your TV set. One is the internet, the other is CEC wired by HDMI, two separate connection types. I don’t think the modem/router is connected to the issue but will be interested in your testing.

The CEC, being wired through the HDMI connection, should be a different beast. After you run the other test, I’d be tempted to suggest that you first check for firmware updates in the TV set (and what make/model is it?) and apply any you find, and then I would seriously think about rebooting the TV’s OS. In most cases I have seen, that requires unplugging the TV from the wall for at least a couple of minutes, and then plugging it back in. 

Thanks for the suggestion.  I checked the TV firmware (Samsung UNK65KS8000) for updates (none available), unplugged the TV and Sonos from power, and unplugged the Internet modem/router. After a couple minutes, I plugged in the modem/router, then plugged in the TV and Sonos. I turned on the TV and the sound worked on the Sonos. So this test was successful. I’ll try some other variations to see what happens. 

I’ll keep my fingers crossed that it keeps working. That reboot sequence between the router and the Sonos can be avoided in the future if you assign reserved IP addresses to your network devices in your router. Details should be in the router’s manual, they all tend to do that process slightly differently. 

Thanks for the suggestion, but I do have a fixed IP address for the Sonos on my LAN. 
Test one. I turned off the power only the router off last night, leaving the TV and Sonos in standby. This morning, I restored power to the router and waited for the Internet to come back up. I first tried music on the Sonos through the app, which worked with no problem. I then paused the music and turned on the TV, but could not get the sound to play until I powered off/on the Sonos and the TV. 
Test two. I put the TV and Sonos into standby and then turned off power to the router. After about 5 minutes I restored power to the router and waited for the Internet to come online. I logged into the router and confirmed the Sonos was online with the same fixed IP address. I then turned on the TV. The Sonos flashed green lights briefly and then the TV sound came on. 
The differences between test one and two are the time the router was off (5 minutes versus overnight), and in test one, I tried music first. Not sure which made the difference. Test two obviously produced the preferred result.