Is it permissible to repeat the mention of the Prophet's name during prayer?

According to the Shafi'is, it is sunnah to invoke blessings upon the Prophet, peace and blessings be upon him, when hearing his name mentioned during prayer. The Malikis permit it to be done silently and without excessive repetition. However, according to the Hanafis, the prayer becomes invalid if invoking blessings upon the Prophet, peace and blessings be upon him, is done in response to hearing his name mentioned.