He suffers from continual emission of madhiy and he uses sticky tape. Does he have to change it for every prayer?

The one who suffers incontinence, whether it involves urine or madhiy, has to do two things:

(i)He has to wash the place and then wrap it with a piece of cloth or a handkerchief to prevent the urine or madhiy spreading.

(ii)He has to do wudu after the time for prayer begins, if anything has come out of him.

He does not have to wash the place and the wrapper again for every prayer, unless he has neglected to take precautions.

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (1/206): The one who suffers from urinary incontinence or a great deal of madhiy that does not stop is like the woman who suffers from irregular and lengthy bleeding: he should do wudoo’ for every prayer, after washing his private parts. The woman who suffers from irregular bleeding, and the one who suffers from urinary incontinence or excessive madhiy, and others like them who continually break their wudoo’ and cannot maintain their tahaarah (purity), have to do wudoo’ for every prayer after washing the site of impurity, wrapping it and trying to avoid emission of that which breaks wudoo’ as much as possible. End quote.

It says in Sharh Muntaha al-Iraadaat (1/120): everyone whose impurity is ongoing, such as a woman with irregular bleeding, or one who has urinary incontinence, or excessive madhiy, or continual breaking of wind, has to wash the site that is contaminated with impurity and wrap it up, i.e., take precautions by doing that which will prevent emission as much as possible, such as using a cotton pad or tying it with a clean piece of cloth. But he does not have to repeat it, meaning washing and wrapping for every prayer, if there has been no negligence on his part, because this condition is overwhelming and complete precautions cannot be taken against it. So the one whose cause of impurity is ongoing should do wudoo’ at the time of every prayer if something comes out. End quote.

Some fuqaha’ do not think that it is obligatory to wrap it and tie a piece of cloth.

Al-Hattaab al-Maaliki (may Allah have mercy on him) said in al-Mudawwanah: It is mustahabb to take precautions by wrapping it with a piece of cloth. Sanad said: It is not obligatory, because he is going to pray with the piece of cloth on which there is some impurity, just as he would pray in his contaminated clothes if he did not use it. Sanad said: Is it mustahabb to change the cloth? Al-Ibyaani said: It is mustahabb for him to do that at the time of prayer and wash it, but according to Sahnoon, it is not mustahabb, and washing the private parts is easier for him than that. End quote from Mawaahib al-Jaleel (1/143).

As you are putting a piece of sticky tape to prevent the madhiy spreading, this is appropriate protection and you do not have to change the tape for every prayer.

And Allah knows best.