The phrase simply means that crises are coming so fast, there seems to be a new one every hour. (It's figurative language; there isn't really a new crisis every 60 minutes – but it seems that way.)
In an office environment, a related metaphor sometimes used is firefighting, which is used to describe a work pace so hectic that people are just “putting out one fire” when the next one starts. For example, in a piece called How Daily Firefighting Affects Your Work Performance, one blogger wrote:
These guys are so brilliant and so efficient that they land up fire fighting, handling emergencies and crises all day. Their own work gets hampered .. after all, you get promoted when you shine at your own work and rarely for salvaging other people's slack.
If you were looking for a word to use around your workplace to describe a pace of crises so frantic that it's hard to do any strategic planning, I think you'd find that fire fighting would be more familiar than crisis-an-hour (at least here in the U.S.), although both would be readily understood.
As a footnote, I don't think that a "crisis mentality" quite means "someone who is always thinking the worst will happen" (that's more of a pessimistic mentality). It's more a matter of acting as though even a minor obstacle is a major crisis. Interestingly enough, one proposed definition at Collins was a "state of continuous panic when challenged," but that proposal was rejected on the grounds that the meaning could be deduced by the individual words. (I'm not sure I completely agree.)