Praise be to Allah.
Madhiy is najas (an impure substance) according to the scholars, and it breaks wudoo’. But if it happens continually and does not stop, then the ruling in this case is that of incontinence and of istihaadah (prolonged irregular vaginal bleeding) in women. In such cases, if a Muslim wants to do tawaaf, he should put something over his private part that will prevent the emission from spreading further, then he should do tawaaf or pray regardless to his circumstances. His previous tawaaf is valid and the ruling on that is the same as one who prays with something impure on him that he has forgotten about; his prayer is valid and the ruling on one who has forgotten is the same as the ruling on one who is unaware of the ruling.
Shaykh ‘Abd al-Kareem al-Khudayr
Repeated emission of madhiy may be because of sickness, the ruling on which is explained above; or it may be because of desire, thinking about and touching women.
The Muslim has to beware of that and exercise great caution when he is performing tawaaf around the House of Allaah. He has to avoid the things that may cause it to be emitted, and he has to fear Allaah. And Allaah is Able to do all things.