Any particular reason to have three sub-tables modify the final force loyalty table, rather than starting with the final loyalty table result and having that modify subsequent rolls on the three sub-tables?
Are these tables supposed to reflect the actual distribution of such units within a military, or to reflect the distribution of units within some subset of a military (e.g., those that commonly see action), or are they skewed for variety, or skewed to balance the sphere-spanning game tier, or what?
On the Training table, "Advanced" represents exceptional training such as the Kensai Kami. But, looking at the Kensai Kami's admission requirements and class sizes, a 3/36 chance of receiving the majority of your personnel from such a program seems absurdly generous for a battalion sized unit and impossibly generous for a regiment. Are these tables supposed to address company and lance-sized units as well? If so, then you might want to have larger (battalion and regiment) sized forces apply a moderating effect to the roll. (While a faction might have one such regiment, its loyalty is not going to be random.)
It seems fair to assume that a unit's prestige is closely tied to the prestige of its typical postings. But if the "Location" table has no effect outside of determining Force Loyalty, then it seems to be acting primarily as a proxy for the unit's supply situation, and I'd rather know the supply situation. (Though if "Location" means something outside of determining Force Loyalty, it might be nice to have both Location and Supply, although that's probably more the realm of whatever detailed resource allocation system was mentioned.)
I would imagine that recent casualties would have a rather large effect on a force's loyalty. In the books, it tends to be tied up with the prestigiousness of the unit's subsequent deployment, their supply situation, how much rest & refit they're getting, and so on. If that's all covered in "Fatigue," then Fatigue should either feed back into loyalty or affect many of the same rolls that loyalty does.