i think it is unhealthy to stay hooked in to work while you are on vacation. completely disconnect. unless you have agreed to some strange arrangement where you are on call while being on vacation (doesn't sound like much of a vacation to me).

separately from this, the company needs to figure out a sustainable plan for how the infrastructure is going to be maintained if you are not available for one reason or another. you might need to call this out to the powers that be if they're not keenly aware of the risks already.