The way letters sent to Ministers work, they are looked at by the Ministers office, the part of the department that deals with the issue is asked to produce a reply, and its then approved and sent by the Ministers office.
Sending 3 letters doesnt mean 3 responses, it just means that one desk officer will get stiffed 3 times. Writing to a Minister doesnt do very much beyond ensuring you get a formal letter back, written by a usually highly overworked officer or civil servant rather than by the Minister in question.