Is it permissible for a woman afflicted with obsessive doubts and the feeling of urine dripping after ablution to pray the next obligatory prayer with the same ablution, or must she perform ablution for each prayer?

It appears that the questioner is afflicted with waswasah (obsessive whispering). The fundamental principle is that she remains in a state of purity unless she is certain that something has exited, based on the Prophet's (peace be upon him) saying: "If any of you finds something in his belly and is unsure whether something has exited or not, he should not leave the mosque until he hears a sound or perceives a smell," and his saying: "Satan comes to one of you during his prayer and blows into his posterior, making him imagine that he has invalidated his ablution when he has not. If he experiences this, he should not stop praying until he hears a sound or perceives a smell." Therefore, one should not surrender to such waswasah. As long as she is not afflicted with urinary incontinence, she can pray with that ablution unless it is invalidated.