It's a 27" Betson Imperial, model is 2914, it's a digital trisync monitor. My thought is the same, if it's flashing an 'out of range' message it's not damaging the monitor.
Any thoughts on the wireless power button? I've read that fluxuations in power can cause damage and so some people avoid things like smart power strips with arcade monitors. I've always used one and haven't had an issue. A button like this doesn't seem like it'd be an issue unless you powered it on/off quickly and repeatedly.