Is your deck sitting on new soil from a newer house? Do you have any idea how deep the current footers go? If you're in a part of the US that freezes in the winter you'll want to go down 42" or more. Most two-man auger bits only go 48".
Could the problem be poor drainage? Do you have water that sits in that area that would be eroding soil away.
You could dig 48" on your footings, pour new footings, jack your current deck temporarily while the footings dry and and then attach post to sit on top of your footings.