Here is a good question, why is Mandarin Iron Man's arch nemesis? Is there a reason beyond the fact he is the most reoccurring villain from the Silver Age.
It seems like most of the iconic Iron Man stories have nothing to do with Mandarin: Doomsquest, Tony stark vs. Obadiah Stane, Demon in a Bottle, Extremist, Armor Wars, etc.
I think Mandarin had one good story recently, but overall how how many great Mandarin stories have there been?
This isn't a new problem, writers have been struggling with what to do with Mandarin for a while, David Michelinie, the man who reinvented Iron Man back in the 80s and made Iron Man the character he is today, didn't use Mandarin because he couldn't think of a way to update him. So this was a problem back in the 80s, with the guy who was responsible for making Iron Man such a compelling character.
Also every time Mandarin gets adapted to other media, they try to change him to deal with the fact he is outdated: the 94 cartoon turned him into some white guy named Arnold Brock who was turned green by the rings, the more recent CGI cartoon turned him into a more sympathetic teenage book worm type and the 2007 Iron Man DTV turned him into Sauron from Lord of the Rings.
It seems like Marvel is struggling more with Mandarin then other major Marvel villains, which is why he is not used as constantly. I think its hard for Mandarin to escape his Yellow Peril origins, even the name is kinda problematic, it sounds like something a white guy would look an Asian character to establish he is Asian. Its like naming an American character " Hank Apple Pie Base Ball Player".
Also do Iron Man and Mandarin have a lot of interesting personal chemistry? There doesn't seem to be anything to connect them in their back story, like say Dr. Doom and Reed Richards or Xavier and Magneto, it seems like Mandarin just showed up one day to try and take over the world and Iron Man decided to stop him. Has Mandarin ever done anything to truly hurt Iron Man? Obadiah Stane managed to steal his company and Zeke Stane managed to nearly kill Pepper.