On my first character, I got asked to do two favors in Whiterun, one involving a bard and one involving a sword. However, on every other character that I have made, I haven't been able to get those favors. I'm pretty sure I've made at least three characters after that. After seeing people complain about not being able to get Shahvee's favor in order to marry her, I wonder. Does the game simply prevent you from getting asked every favor in the game? If not, why haven't I been able to get asked those favors on my other character?

Does anybody know?

Radiant story makes the favor random I believe

There are Radiant Quests and there are Scripted or Static Quests. Radiant Quests are purely random but based on what you have done with other quests, Scripted Quests are based on another quest's completion or your level or some other action that will trigger it, then there are the Static Quests that are always there, no matter what you do.

In other words, it is possible to play the game twice and only repeat some of the quests.