There are any number of reasons they could be going offline. Do they stay breathing cyan, or switch to breathing green? If breathing green happens, its blocking the loop (or not using threading).
A bad Internet connection could cause problems as well, as the Photon likes to keep the connection open. Every time the connection is interrupted, you’ll go offline.
The same thing can happen with Wi-Fi if you have a bad Wi-Fi signal, or a problem with your Wi-Fi access point.
The best way to troubleshoot this is to get a log while connected by USB. This will sometimes show what’s causing the disconnection.