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The best time to get an income protection policy (or any other form of coverage) is to get it immediately just prior to a disability!
Seriously, even though that is not an inaccurate answer, the best time to get coverage is at the earliest possible moment–when it is both financially feasible and practical (even though there may not be an obvious need at the moment).
The reason is, health can change, circumstances can change, and so on.
Why, then, do people wait until it is too late to buy this valuable insurance?
One reason might be that they dont see the need for it. Another reason might be that no one told them they should have disability insurance or that this form of protection even exists. They also could have a (false) belief that they will never get disabled or that their employer will pay their expenses if they do.
To dispel some of these notions, refer to the chart on this page. It statistically points out that disability happens, even at young ages.
What happens if someone wants coverage but already has been turned down for any number of reasons and not necessarily due to health? Is the "best" time gone? No, not if the agent knows where to go for assistance and a probable solution. There are brokers who do specialize in hard-to-place cases.
In general, though, the best time to obtain disability insurance is at the earliest possible moment. As the chart shows, the sooner the better.