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What do you mean by thermostat went out? Is thermostat completely defective and inoperable or dies screen go blank and come back on?
Sounds like there could be an issue such as power spikes taking thermostat out. Did all functions seem to work properly after they replaced the first time?What is model on thermostat?
A power spike is what happens when you notice your lights get brighter for a second or two. Transformer from utility company jumps above the normal 120v per leg of power.
Only way I can think of wiring would effect it is if old and brittle and wires actually shorted together.
Battery or hard wired should not make a difference.