Best answer by Airgetlam
And it's important that you used the word BRIDGE in your system. The BRIDGE is old enough at this point to occasionally suffer from a problem with voltage in the power supply. Fortunately, this is relatively easy to test. Unplug your BRIDGE from power, and from the ethernet cable. Run the ethernet cable to one of your speakers, instead. Since this is a temporary test, it's OK to move one of the speakers. If your system shows up, you've defined the problem is with the BRIDGE, since when a speaker is connected, it acts in the same way as a BRIDGE.
You can purchase replacement power supplies for the BRIDGE many places, including Amazon. Or, you can replace your BRIDGE with a BOOST, which is a newer and slightly better version of the BRIDGE, or you can just dump your BRIDGE altogether, and either leave an ethernet cable connected to a speaker, or go to wireless mode, where the speakers use your own wifi signal, rather than their own SonosNet signal. My preference when I did this was to get a BOOST.
However, that's not the only potential issue that might cause your speakers to be dropping off your LAN. It could be as simple as wifi interference, or even a duplicate IP address issue. Duplicate IP address issues often show up after the Sonos software updates, due to the process involved. It's easily rectified by unplugging your Sonos devices (all of them!) and rebooting your router. Once the router comes back up, plug back in your Sonos devices.
Hope one of these potentials help you. If not, I would recommend that you submit a system diagnostic within 10 minutes of recreating this issue, and either post the number here, or contact Sonos to discuss it. I tend to suggest the phone folks, they have more tools available, but are only available during business hours. Both the Twitter and Facebook support folks are available 24/7.
There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.