When a control/thermostat disconnects from the internet server or from its Wi-Fi router, it will usually re-connect by itself when the cause of the interruption has cleared.
Sometimes, however, they don't re-connect. If the disconnect includes the Wi-Fi network as well as the server, then the SSID and password may have been lost in the outage. Re-entering these may solve the problem.
If that doesn't fix the issue, then power-cycling should be tried. In some cases a power off/on cycle will enable the unit to re-connect. This is accomplished by separating the body of the control from the base and then re-attaching.
For Infinity/Evolution -A controls there are two tabs on top that, when pressed, allow the body to be separated from the base.
All the other types, including the Infinity/Evolution -B controls, can be cycled by gently pulling the body to unsnap it from the base or by inserting a screwdriver into a small slot and twisting slightly to unsnap the body from the base. When re-attaching, be careful to line up all the pins and sockets before gently snapping the body onto the base.
If a homeowner needs to do the power cycling, they should do it by turning off the HVAC system breaker for a few seconds and then turning it back on. We don't want to risk damage by having the homeowner remove the front of the control/thermostat and then replace it, since it is very easy to bend the connector pins.