Is it not enough to furnish the Form only once at the time of placing the deposit?

Is it not enough to furnish the Form only once at the time of placing the deposit?

No, Form 15G/H will have to be submitted at the beginning of each financial year covering all the existing deposits.
If new deposits are to be made during the year, then a new Form 15G/H will have to be submitted. Also, if there are any changes in the Income Tax laws, then a new form 15G/H would be required to be submitted.