Sorry for a double post, but I think I need to clarify a bit. The entire deck was previously painted instead of stained or sealed.

While I don't know anything about restoring a deck, I do have a large deck with peeling paint on the house I bought last year. In our case, apparently the deck was not prepped correctly prior to being painted. Just made pretty to sell the house. The painter I consulted would power wash, sand, and then paint (two coats) in that order. One coat of paint might be sufficient if repainting with the same color. I was told that once a deck is painted, there is no going back to a natural finish.

That's unfortunate, because a deck [with space between the boards] is not a good place for paint. Stain a deck, paint a porch floor.
Now that you have paint though, I think the painter has it right. If you are using water based paint, you MUST have 2 finish coats.

First you need to remove all the old "paint" from the deck. Strip it with HD-80 or Rip-It and a power washer. Done correctly with the correct concentration of NaOH will remove all the finish and you will not need to sand. Sanding of some PTW is not good for the lungs as it releases chemicals into the air. Follow the stripping with neutralizer(acid) to bring the ph of the wood back to normal. Before you apply the stripper spray water all around the deck area so it will not kill grass and plants. Allow it to dry and coat it with a quality deck sealer.
Ready Seal, Armstrong Clark are my choices in 95% of the decks I work on.