There's several possibilities. You didn't state whether by "0.1 phosphate" you mean 0.1 ppm phosphate. If that's the case, and you're actually stating your phosphate level (instead of phosphorus level - multiply by 3 if your test gives you phosphorus concentration instead of phosphate), then you'd have about 100 ppb phosphate. That level is within the desired range for a reef tank, and especially if you have sensitive stony coral species like acropora, I wouldn't recommend reducing it. Especially if it's done quickly.
From the standpoint of the explanation of why the phosphate level isn't changing, it's possible that your test is near its lower limit of sensitivity. That would be the case for the almost all tests on the market except for the Hanna checker tests. If you are using a Hanna Checker ultra-low-range phosphate meter (which should yield accurate results in the 100ppb range), it may simply be that the rate of phosphate addition that you're introducing with food is the same (roughly) as you're taking out with your skimmer and chaeto.