What are the proposed methods for transferring people from orbiting spacecraft to Mars surface specifically if multiple trips are required. Are there any that don't require a new heat shield for each descent?
The Shuttle didn't require a new heat shield each time, just refurbishment. As far as I know, SpaceX are working with Mars in mind. Their Dragon seems to be built with such reusability in mind. I haven't found much on this but this article seems to confirm this:
All of SpaceX's initial production will be used for domestic in-house applications including the heat shields of the Dragon spacecraft, and the Falcon 9 second stage, which is designed to return from orbit for recovery and reuse.
Frankly, if there's anyone out there that does it I'd bet on SpaceX.
According to this article, the PICA-X heat shield on SpaceX's Dragon ablates less than 15% on a single Earth reentry. I assume that Mars's thinner atmosphere and lower gravity (-> lower orbital speed) implies that there would be even less ablation in a Mars entry.