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Hiccup mode is a protection for the regulator when there is a short circuit on the output.
The IC disconnects the output and asserts the output for a small period of time so that it can see if the short circuit remains.
If it senses a high current on the output, which means a short circuit it cuts the current again and retry after some moment (can be controlled on some IC's).
If it senses a regular current on the output, it can return to normal operation.
When it's looked on the osciloscope these series of retries looks like a hiccup, that's why it gets its name.
Hiccup