The problem here is that the PutItem command does overwrite exiting items if they are the same. So every time you try to insert Update= Done it overwrites the same item. So you need to put something unique in your item so that a new item is created and the old one is not overwritten. You could use either UUID or the time of execution.
from datetime import datetime
[...]
table.put_item(
Item = {
"Update": response,
"ProcessingTime": datetime.now().isoformat()
}
)