I'm not familiar with "unyielding advance", but "fighting chance" is your HO trigger as I remember it. It's the one you got from your fighter archtype at around level 4 I think and all fighters have it. According to a post I saw from a dev, certain abilities (the HO trigger for example) are not upgradable.
Basically, any ability that simply has some sort of utility effect, you can expect to not be upgraded. The home city recall ability you get with citizenship is another example.
Of course, I'm not telling you not to look for upgrades.. just don't expect to find upgrades for absolutely everything =)