I have to agree that Dot Tune is pretty unreliable. There is no direct correlation between when AF is confirmed by the firmware, and the AFMA setting. AF confirmation is a bit more arbitrary, which is why there is variability.
When you use FoCal, do you use the maximum samples option? I forget what it is exactly, I think 10 samples are taken per AFMA setting. If you only do the "quick" AFMA tuning with FoCal, which only uses 2 or 3 samples per AFMA setting, it isn't really all that much better than Dot Tune. You really need to use a high number of samples to get accurate results. Small things during the AFMA tuning process, such as a missfocus (which do happen), wins or something else that might temporarily change the focus distance, etc. can all mess with the focus hits at each AFMA setting. By doing at least 10 samples per, FoCal is then able to use some basic statistics to discard outliers and produce a more accurate curve, and thus find the most accurate AFMA setting.
That said, AF IS often distance dependent. This could be due to spherical aberration in a lens, or possibly other aspects of lens construction. Regardless of the why, tuning AFMA for near focus will often result in improper AFMA for far focus. You might want to run FoCal with a high sample count for both near and far focus, and just try to memorize the settings, or write them down and keep the settings in your camera bag, or something like that, so you can reset AFMA if you need to switch periodically between far and near focus.