You can make the break marks not disappear on blocks by breaking a instant breaking block on top of the block.
These can be removed by starting breaking the block again.
The break marks also disappear after some time, but only visually. If you continue the process, they start at the same level again.
This can be tested by placing farmland and rapidly placing and braking carrots or similar on the farmland.
Examples can be found in the attachments.
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Duplicate of MC-157404.