Not a definite mate no. As I said, I've never actually looked into it or tested it or anything like that so I can't say 100% sure. My answer is based mainly on the fact that in my houndsmoor city which is now inactive I had supplies on a 24 hour run. I logged in 24 hours after they would have been available for collection (48 hours after the time I set them) so I could dump FP in a GB and they were still there and available (I didn't collect because I couldn't be bothered to reset them and I was in a rush lol). I then logged in again the following day, a few minutes earlier, to again dump FP. While I was logged in I watched as the supplies began to go stale and it was around 72 hours total since I had set the supplies meaning that after the 24 hour time I set for them, they lasted another 48 hours after that until they went stale, which from the time I set them to the time they went stale would be 3x the set time.
Again I can't be certain but hopefully this will give a rough time scale for you
. I would however suggest that you try to calculate the times you set your supplies for in order to fit a time in which you know you will be able to collect them. This will prevent them going stale and also prevent plunder from neighbours