Another way to achieve this is by using the Automation action “Wait for time to pass (delay)” and change the delay setting to reference your input_number.state as such:
delay:
milliseconds: '{{ states.input_number.remote_pulse_time.state | int }}'
You’ll have to swap from the visual editor to the YAML editor to modify it but this is an easy way to achieve the solution.
I’m assuming you mean the accumulated delay doesn’t survive? As in the current count of the delayed time will reset to 0 on a reboot, not the preset delay time.
Correct, when you set a delay in an automation a reboot will reset the delay but also anything that was supposed happen after the delay will also not happen. This may/may not be a problem for some but if you want to ensure your delayed action happens it’s better to setup a Timer helper that is started, which will survive a reboot, and then you can trigger based on that timer finishing.