Favorable ratings help out immensely during a crisis. It can serve as the good will or good credit that organizations can rely upon and turn to when the client feels threatened with a risk or company crisis. The idea of being able to have garnered more credit will allow the customer to trust the organization when crises emerge and not quickly turn and run from them. Conversely, when companies have not developed this good will or good credit from customers, the slightest hint of challenging situations will prompt the customer's immediate departure, causing a loss of business. Part of the reason why established organizations are able to weather through and endure challenging situations is because of their good reputation developed prior to it. For example, if Toyota had an awful reputation prior to their recent recall challenges, the company would be in an even worse predicament than they are currently. It is only because they have been able to develop so much good will and credit with the consumer that they can "cash it in" at this time, when they sorely need to do so.
The title give to the question., and the question it self do not seem to go well together.
To begin with crisis and risk management are two very distinctly separate functions. Risk management refers to actions that a company may take to reduce the losses incurred in future due to uncertainty of future developments and events. Crisis management refers to the way of dealing with a sudden major problem that need to be solved or suitably handled quickly.
Now coming to the main question, it is important that the way of handling a crisis and the implication of past reputation on appropriate response to a crisis will very much depend on the nature of crisis. For some types of crisis the past reputation may not have much implication while in others types of crisis it will make a big difference. For example if the crisis situation has been developed by a fire in the manufacturing plant the reputation of the company does not play very important role in nature of solution. But if the crisis has developed by a large consignment of a product of a food manufacturing company found to be infected, the reputation of a company will play a major role in determining the right approach to the crisis.
In general a good reputation may make handling of the crisis easier or difficult depending on the situation. A good reputation may increase the severity of a crisis when it tend to tarnish the good image of the company. In other case a good image among general may become an asset in handling opposition by a small but powerful group of people.