The reason your cucumber plants are turning white is that the soil is to rich in fertilizer, mainly nitrogen. Try digging up your plants, dig a large hole around where they were and fill it in with regular non-fertilized topsoil, then replant your cucumbers. They should soon start to thrive.
The whitening of cucumber leaves is caused by powdery mildew which is a fungal disease that becomes most severe during the late summer and fall planting seasons. Try growing varieties that are resistant to the fungal attack.