Is it obligatory to repeat the prayer if one feels madhiy (urethral discharge) coming out whilst praying?

Merely thinking that something has happened that invalidates wudu, or not being certain of it, is not regarded as invalidating the state of purity and the prayer. Rather that ruling only comes into effect if the accountable individual is certain or thinks it most likely that something has come out of him, because the Prophet (blessings and peace of Allah be upon him) said concerning a man who kept thinking that he had invalidated his wudu: “Do not stop (praying) unless you hear a sound or notice a smell.” Narrated by Muslim. 

Secondly: 

If a person constantly experiences something that invalidates his wudu, and it is ongoing and does not stop, then he comes under the same ruling as a woman who suffers istihaadah (ongoing non-menstrual bleeding): she may offer whatever prayers she wants so long as the time for prayer has not ended, even if something comes out of her during the prayer, because she cannot help it., And if she waits until the end of the time or until the time is almost over, that will not help her at all. Allah, may He be exalted, says (interpretation of the meaning): “So keep your duty to Allah and fear Him as much as you can” [at-Taghaabun 64:16]. 

But if the matter that invalidates his wudu is intermittent and does not happen all the time – rather it happens sometimes and stops sometimes – then he has to pray in a state of complete purity, even if that means waiting until near the end of the time for the prayer. He has to wait until that issue stops. 

Thus it becomes clear that there is a difference between the case of the woman who suffered istihaadah and that of ‘Ali (may Allah be pleased with him), because that woman came and complained that the bleeding in her case was continuous, hence the hadith tells us that she said: “I am a woman who suffers ongoing non-menstrual bleeding and I never become pure, so should I stop praying?” (Agreed upon). 

But in the case of ‘Ali (may Allah be pleased with him), the issue that invalidated his wudu was not continuous, rather it was intermittent, based on the fact that he (may Allah be pleased with him) said: “I was a man who emitted a great deal of urethral discharge” (agreed upon) – i.e., he emitted a great deal of madhiy. This does not mean that he constantly emitted madhiy, unlike the woman who suffered istihaadah, as she said: “I never become pure”, i.e., she never stopped bleeding. 

To sum up: with regard to the man who emits madhiy, if his situation is what is usually the case, that he emits it sometimes, then it stops, then he should go about purifying himself like anyone else. Whenever he emits madhiy, he should wash his penis and testicles, and wash off anything that has got on to his clothes, then do wudu. If anything comes out of him whilst he is praying, his wudu and prayer become invalid. 

But if he is incontinent in this sense, as it were, and he emits madhiy all the time, then he should approach the matter of purifying himself like those who have excuses. 

For more information, please see the answers to questions no. 22843 and 126293

And Allah knows best.