بسم الله الرحمن الرحيم
If the drops continue to such a great extent that the said person does not get a time that he could offer fardh salah after making wudhu and this situation remains during the whole time of salah. Then in such a case the said person shall be deemed excused as per the Shariah. So, for him, the ruling is that he will make wudhu for each salah and will offer as much fardh and nafl salah as he wishes with that wudhu, but as soon as the time of salah passes his wudhu shall break and new wudhu should be made to offer the next salah. There are some details in the rulings of excused person, hence it is better that the said person narrates his whole situation to some expert Alim or Mufti and follows the instructions given by him.
وصاحب عذر من به سلسل بول ، إن استوعب عذره تمام وقت صلاة مفروضة بأن لا يجد في جميع وقتها زمنا يتوضأ ويصلي خاليا عن الحدث . (شامي 1/504 زكريا) (مستفاد:فتاوى محموديه ، جديد ڈابھیل 5/217، 216، 220، 221، 6/ 285، بهشتي زيور 1/54، احسن الفتاوى زكريا 2/74، 75).
Allah knows Best!
Darul Uloom Deoband