Is it permissible for my mother, who suffers from heart disease, diabetes, and high blood pressure, and who experiences urinary incontinence to the extent that she wets herself and is unable to change her clothes for each prayer, to stop praying due to her inability to purify herself?

One who cannot control their urine (suffering from سلس al-salas, incontinence) should perform ablution (wudu') for each prayer after its time has begun, and the emission of urine during prayer does not harm them. The principle is that the private parts should be bound with something that prevents the spread of urine, such as a diaper. It is not necessary to change it for every prayer if it is securely fastened. Some scholars, like the Malikis, hold the view that wearing a bandage is not obligatory. Your mother may adopt this opinion if changing the diaper is difficult for her. She must use a clean garment for her prayer, and she is not permitted to abandon prayer under any circumstances. She may combine two prayers (Dhuhr and Asr, Maghrib and Isha) as a concession to alleviate her burden.