All things equal, I think that developing and maintaining productive, long-term relationships with insurers is preferable to switching insurers after a large loss in order to receive a premium lower than the incumbent will offer you on renewal. Unfortunately, seldom are "all things equal."
A single large loss often triggers surcharges in addition to normal rate adjustments for many underwriters, particularly for their policyholders of short duration. Given this and since many policyholders are driven more by price than by loyalty to their brokers or insurers (and vice versa), it is important to examine whether or not a policyholder should move insurers (or brokers) based on price regardless of relationship.
Managing risk among policyholders, insurers, and brokers is fundamental. Uberrima fides (the doctrine of utmost good faith) requires the insured to reveal the exact nature and potential of the risks transferred to the insurer and the insurer to ensure that its policy fits the needs of and benefits the insured. A broker should help its customers understand the factors affecting their premium and what actions they can take to manage proactively the risks within their control. After a significant single large claim, the insurance customer should tap the expertise of the insurer and the broker to learn more about managing its cost of risk and to formulate a plan to stabilize immediate and medium-term premium increases (i.e,. to avoid "one big hit" on premium).
If this doesn't occur, then one should consider a switch.
The cons of switching carriers include (1) the limited number of competing insurers and pools in the marketplace catering to your type of risk and (2) the increased
potential for unavailability of insurance during hard market cycles.
The pros of switching carriers include (1) immediate short-term cost savings and (2) the fresh perspective of new underwriters.