If petunias begin to wilt, they most likely have a health problem that requires attention. Wilting petunias are suffering from one or more issues that make them susceptible to other diseases or pest problems that can weaken the plants or shorten their lifespan and destroy that season's blossoms.

...
Healthy petunias have bright flowers and unfurled leaves.

Insect Problems

There are a number of garden pests that prey on petunias, including aphids and slugs. Aphids feed on the leaves of the petunia, leaving open wounds that invite disease to damage the flowers further. Controlling aphids with pesticides keeps the petunias healthy and growing. Slugs also feed on petunias, making the plant weaker and more susceptible to damage. Slugs can be drawn away from the petunias with the use of specially baited traps that help remove them from the garden.

Fungal Diseases

Fungal diseases can cause a petunia plant to wilt. If moisture builds up or sits on the leaves of the petunia, the potential for fungal problems increases. Fungi damage petunias in a number of ways, weakening the plant and causing them to droop and sag as they die. Water petunias in the morning to prevent water from sitting on the leaves during the day and apply a fungicide if signs of infection occur. Some signs of fungal problems include wilt and spots on the leaves or stems of the petunia.

Water

Watering a petunia properly is key to its health. Too much and too little water are equally damaging to the petunia plant and both cause it to wilt and droop. Too little water dries out the soil and prevents the plant from taking in nutrients. Dehydration causes the leaves to dry up and wilt, as well as turning brown at the edges. Too much water suffocates the roots of the petunia, causing the plant to swell and then droop as it is drowned.

Sunlight

The amount of light a petunia plant receives affects the health of the plant. Petunias thrive in full sunlight, but they will tolerate partial shade as long as they receive five to six hours of sunlight each day. Less light than that prevents the petunias from receiving the energy they need to grow, causing them to become straggly and weak. Petunias growing in weak or low sunlight are more likely to exhibit signs of wilting.