Hi CC,
We usually advise to grit your teeth and wait another day until ammonia is a true zero ppm before adding ammonia at your usual "add-hour" out of the 24 hour day. Sometimes I think this lets everything get down to zero for a bit and might be good but this is pure speculation. However, if it were to still sit at .25ppm tomorrow I'd probably go ahead and add back to 4ppm or so. There is a "sticking" syndrome we often see near the end where one or the other of ammonia or nitrite(NO2) will just persist in showing some (usually fairly small) amount day after day. I don' pretend to understand it, its just an observation and another observation is that it will eventually go away if one simply proceeds as normal.
Now, about that "why?" question I hear you asking in your comment about the timing of ammonia vs. nitrite(NO2)... With these questions I think it always helps to step back and visualize a graph with quantities of the substances on the vertical axis and time on the horizontal axis and picture that our nitrogen passes along from left to right as a hump. First we squirt in our milliliters of ammonia, creating the hump, then the A-Bacs move the hump to the right, changing it to nitrite(NO2) and the N-Bacs chomp on it and move it to the right creating NO3.
Now when we take a battery of tests with our test kit and log them in our aquarium notebook, we are taking a momentary "snapshot" in time. We really have no idea at that moment whether the value we see is a point on an up slope or on a down slope. If our ammonia was always added at the same time of day and our tests were always taking at the same time of day then we have added confidence about the regularity of our snapshots...but....
If we do anything like water changes or changes to our test times, just as examples, then we'd expect our humps we're graphing and/or the consistency of our snapshot sequence to blur and be less understandable. Of course, on top of that, not even the best of the bacteriologists would tell you they fully understand the life cycle the biofilm structures that each bacterial species builds, much less how it might be effected by other species working nearby or other tank factors.
The "end game" of fishless cycling can be just as unpredictable as the other phases (eg. nitrite spike phase seeming to take too long, initial drop of ammonia seeming to take forever) but that's just a characteristic of "in vitro biology" (to put a good sounding but wrong name on it, lol) rather than "chemistry lab."
~~waterdrop~~