When is it recommended to do one wudu after another?

Firstly:

It is Sunnah to renew wudu even when one still has wudu, according to the majority of scholars, including the four imams. This is indicated by a number of hadiths, including the following:

The report narrated by al-Bukhari (214) from Anas ibn Maalik (may Allah be pleased with him), who said: The Prophet (blessings and peace of Allah be upon him) used to do wudu for every prayer. At-Tirmidhi (58) added: whether he was in a state of purity or not.

An-Nawawi (may Allah have mercy on him) said: Our companions are agreed that it is recommended to renew wudu, which means when a person’s wudu is still valid and he does wudu again without having invalidated his wudu. End quote.

See: al-Majmoo‘ (1/495), al-Mughni (1/96) and al-Mawsoo‘ah al-Fiqhiyyah (10/155).

Secondly:

When is it recommended to renew wudu? There are several scholarly views. An-Nawawi (may Allah have mercy on him) said: The most correct view in our madhhab is: If he prayed with the first wudu, whether the prayer was obligatory or supererogatory. End quote.

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said in ash-Sharh al-Mumti‘: Renewing wudu may be Sunnah, if the person prayed with the wudu he did previously. If he prayed with the wudu he did previously, then it is recommended for him to do wudu again for the next prayer.

For example, someone did wudu for Zuhr and prayed Zuhr, then the time for ‘Asr came and he was still in a state of purity. In that case, it is Sunnah for him to do a new wudu, because he already prayed with the previous wudu. So renewing wudu for ‘Asr is something prescribed. If he did not pray with it, meaning that he did wudu for ‘Asr before the time for the prayer began, and did not pray with this wudu, then when the adhaan was given for ‘Asr he renewed this wudu, this is not prescribed, because he did not pray with the first wudu… End quote.

And Allah knows best.