What is the longest period you can keep you Wudu if you are a person that continues breaking it (gastro problem - winds)?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Breaking wind continuously with no considerable intervals in which one could perform his ablution and prayers before the fixed time of the prayer ends (without passing wind) has no influence on the validity of ablution. Hence, a person in such a state performs ablution after the entering of the time of prayer. Then he/she performs the obligatory prayers and any Nawafil he wishes. In this case, passing wind does not have any impact on the validity of Wudu even during prayer as long as he does not do it deliberately. Allah knows best.

For more benefit on the prayer of a person suffering from wind incontinence, please refer to Fataawa 335023, 380521, 380305, and 361699.

Allah knows best.