Reference: ath-Thamar al-Mustataab – Volume 1, Page 31
al-Ikhtiyaaraat al-Fiqhiyyah – Page 67, No.45
Question: Should the tayammum be done (renewed) for every prayer or [is it sufficient] to pray with the [current] tayammum for both the obligatory and voluntary prayers?
Response: So long as he does not find water, he should [continue to] pray with that [tayammum] what he wishes from the obligatory and voluntary prayers.