Is it permissible to pray Dhuhr with heavy discharge that makes it difficult to perform ablution after having performed it to leave the house?

Vaginal discharge invalidates ablution (wudu). If the discharge is continuous throughout the prayer time, you must perform ablution for each prayer after its time has begun. If this discharge is from vaginal secretions, it is pure but invalidates ablution. However, if it is yellowish or brownish (kudrah), it is impure and invalidates ablution. In this case, you must clean yourself (istinja') and purify whatever it has soiled on your clothes and body, while using a piece of cloth to prevent the spread of impurity. It is not necessary to re-bandage the area with each ablution. The majority opinion holds that performing ablution for each prayer and taking precautions (like using a protective cloth) is more safeguard.