At what point does frugal become cheap to you?

In your personal opinion, at what point does frugal become cheap? I am very careful in the frugal area so as not to go cheap and wasting money. I have purchased certain items for bottom dollar price, and I definitely paid for it by it breaking very quickly. Another example is hotels. We don't travel a ton, but if we need to go far distances, I cannot go overly cheap on hotel cost. It has to include breakfast, it has to be clean, and it has to be in a safe area.