Not a definitive answer, but just guessing, based on what I know about how airplane toilets work. And assuming there isn't some mechanical issue, like a clog, that can knock out the system--

The modern vacuum system used on airplanes uses a separate reservoir of fluid used with each flush. The fluid doesn't come from the holding tank, as it does on older systems. Once that reservoir is dry, it is difficult to flush any solid waste. The conjecture part of my answer is that the vacuum pump may actually shut down when the flushing fluid runs dry, so even liquid waste may not be "flushable" at that point.

I guess the other logical answer is that the system shuts down once the holding tanks are full and can't accept any more waste.