Is the first salutation of the the mosque sufficient for one who came, prayed it, then left for a need, or is it permissible for him to pray another?

The jurists have agreed on the permissibility of the Masjid greeting (Tahiyyat al-Masjid), based on the Prophet's (peace be upon him) saying: "When any of you enters the mosque, he should pray two rak'ahs before he sits down." They differed, however, regarding one who repeatedly enters and exits the mosque within short intervals: should he suffice with a single greeting upon his first entry (the view of the Hanafis and Malikis), or is it recommended to repeat it every time he enters (the view of the Shafi'is and Ibn Taymiyyah)? The matter is broad, and whoever performs it every time he enters will have a greater reward.