I expect that the vet has suggested this because some sorts of critical care contain pro-biotics including yeasts which start to ferment once you have added water and left at room temperature for a few hours. Also as already stated, if you keep dipping a syringe back into the main mix that has been in a piggies mouth then you are transferring other bugs that could multiply and spoil the food.
Like spinningnickel I make up a batch of thick paste (personally I use the piggies own nuggets with added Vit C and probiotcs, soaked in warm boiled water and then blended with a hand blender - much cheaper and they prefer it) . This is stored in the fridge in an airtight container over a period of 24hours. I decant what I need into a seperate clean dish each time , add some warm boiled water and maybe, depending upon the pig, some Ellas Organic baby food, and then syringe this, throwing away any that remains.
If you are syringing a pig that isn;t eating at all you need to aim for 120ml in 24hours - that's 20-30ml max stomach capacity per feed spread 3-4 hours apart (to give their stomach time to empty bewteen meals). It also helps to syringe some water after every 3-4 syringes of mush to help rinse their mouths !
If the pig isn;t pooping very well, producing tiny poops or is not pooping at all then you need to go back to the vet to get some oral gut simulants - metoclo-promide (or eme-prid) and zan-tac are most commonly prescribed. Also ensure that if necessary there is adequate pain relief (normally met-cam) as pain is one of the main resons why piggies stop eating.
Hope this helps
x