I believe you are missing the spirit of making concessions, and worse you are close enough to general understanding of the word 'concede' that many of your critics will purport that you are correct.
cede - relinquish ownership [or control] of (some possession).
concede - resign, cease resistance; ‘to give up’ an argument, standoff, impasse, etc.; withdraw prior contention or opinion from conversation for the sake of moving on.
Pleading 'No Contest' (nolo contendere) in court proceedings is a real-life example of conceding that adequately respects the many facets of the meaning behind the word 'concede': (these are not synonyms but rather ingredients necessary for 'concede' to apply)
- a dispute
- reluctance to change opinion or admit/feign agreement
- Unwillingness to endure a battle of incompatible opinions
- The value of a potential eventual victory is no longer greater than the expected value derived from officially maintaining a conflicting opinion.
Pleading 'No Contest' tells the court that you are aware of the charges and that you do not intend to fight the charges; you thus concede the case and your opponent wins by default. Similarly, conversations and arguments can hit standstills and impasses that prevent the conversation from continuing normally, or even amicably, until someone concedes and decides to give in, whether or not their opinion has been swayed whatsoever.
"Fighting a losing battle" and "throwing good money after bad" are phrases that attempt to highlight the futility of an endeavor, its "rightness" or "wrongness" notwithstanding.
Some commentary on your examples:
I never thought she would concede her XYZ at the end. (Verb)
XYZ in this case can be things like belief, opinion.
XYZ would be something that opponents would be attempting to show to be invalid.
XYZ in this case is notably not anything physical. (You can't concede your wallet or your glasses.)
I did not know if she can be concessible. (Adjective)
Here, 'she' would have to stand for some idea that we endearingly refer to as feminine, like "Lady Liberty".
The party acknowledged concededly. (Adv)
This sounds more like it is meant to describe that "the party reluctantly acknowledged their defeat."
This time of the year, people are more generous and easily concede any special requests. (Grant)
Here, 'accommodate' would be a far better choice than 'concede' for many reasons:
Here, 'requests' are concessible.
All in all:
When that would otherwise be in wait, pending you concede, you are seeking to continue an interaction, situation, or dialogue, even though you may or may o longer agree with the premises.