Does my affliction with constant, odorless, and silent flatulence, which is continuously expelled, necessitate wudu for each prayer after its time has begun, or am I required to perform wudu repeatedly with each occurrence?

If the time of cessation of discharge is not regular and fluctuates, then your ruling is the same as one afflicted with incontinence ( سلس); thus, you must perform ablution (wudu') after the time for prayer begins. You then pray the obligatory prayer and whatever supererogatory prayers you wish with this ablution, and do not pay attention to what exits from you. This is if what you mention is true; we advise you to turn away from whisperings (waswas).