With the overwhelming majority of heat shields being ablative and expendable in nature, it is fascinating to read about the Shuttle's TPS, its design and some of the problems that it faced. I believe that at some point in the (likely distant) future, developing reusable heat shielding systems will be of interest. Assuming for a moment that my speculation is accurate (please comment if you think that it is not), what would be the primary design challenges facing such a development?
Making it cost effective
One of the large expenses in the shuttle program was to inspect and overhaul the heat shield after each flight. A major condition for re-use to be feasible is that the equipment is expensive, and still useful after flight. Even if they are specialized and single-purpose, thermal tiles are not exactly expensive to manufacture, and may benefit more from a higher production rate than re-use. (A small market for used shuttle tiles seems to exist, but it is not that important for the overall economy.)
Another issue is reliability, you have to be tediously careful to find that one invisible crack or weakening that may end in a catastrophe. A heat shield defect is not something to be careless about, and to guaranty quality, an enormous amount of manual labour is required.
We remember Columbia
Hohmannfan detailed the basic problem behind developing a fully reusable heat shield.
I believe a more viable alternative developing an inexpensive, simple to apply ablator. Even some kind that an astronaut could spray on, while on a spacewalk or after landing on a planet.
Ablator as such is really not a very complex idea chemically, and leaves a lot of room for improvement in other aspects than 'ablative'. Applying it to shuttle tanks was done by a spray-on method. So - make the firm, hard non-ablative part of the heat shield reusable, but reapply the ablator whenever needed - even in field conditions. Just treat it as consumable like fuel or food, not as a part, like an engine - the heat shield "consumes" ablator, the way engine consumes fuel.
The OP is missing the point of what an ablative heat shield is actually doing.
The heat shield's primary function isn't to protect the capsule. An aerodynamic shell would fare far better than a heat shield.
The main function of a heat shield is to slow a capsule down from orbital velocity.
It does this by converting kinetic energy into a huge amount of heat.
In fact, much of the heat generated never touches the heat shield.
To protect the capsule by pure insulation is rather difficult. As a huge amount of energy needs to be dissipated, or the heat shield would have to insulate the huge temperate differences for the lengthy reentry sequence (over 10 minutes long).
Additionally the skin temperature is at about 1600C, which is above melting point of many materials. Most materials would structurally fail at that temperature.
My point is of course is that you are in effect trying to build a reusable meteorite catcher (in terms of energy).