We had a project like this once or twice when I was landscaping so I asked my uncle for his opinion.
If the source of the problem is erosion/lack of foundation, you can go in from the sides/edges and push more materials underneath with something like a packing bar or a temper/tamper. Just keep pushing more in until you can't. Sand is an option but if you can get ahold of some road base or decomposed granite (something pulverized like that) it will hold better. Sand is more likely to wash out again. It may take a few sessions, letting it settle/open up between to add more, but eventually you will get it reinforced with this method without having to pull the cement up. Just don't get carried away and smash/crack the edge of the deck yourself in the process! 😄
He also suggested checking if there is a broken pipe underneath somewhere too, because that could also be a possible cause. Just-in-case.
RE: On Vacation - can you vacation?