There are so many symbols that are undefined here that I cannot give you a definitive answer (I'm missing, es, s, emax, astar, and NN). I'm assuming that you don't want to provide all of your code because you think it's too complicated, but you either need to provide enough code that I can at least run it, or you need to pare it down to a minimal example that demonstrates the problem.

Also, can you please explain what type of error you're seeing? I don't even know what you think is going wrong. Do you get error messages (and if so, what are they)? Are you getting invalid results?

The place where all of the undefined symbols are is the Which expression. So, I'm guessing that the problem is that one of the conditions in Which is not evaluating to True or False. If a Which encounters a condition that doesn't evaluate to True or False, then it just quits and returns the whole Which expression. For example,

a = "not a number";
Which[
 a > 7, "something",
 True, "something else"]

This will return the full Which unevaluated, because it cannot resolve a > 7 to a truth value.

But that's just a guess.

Well, all I can suggest is that you find a way to ask your question more concretely. There's just no way for me to guess what could be going wrong. I'd need to see what you're trying to do. I'm honestly not even sure how to interpret your question. By "a more complex inner loop" do you mean a different version of SolveInnerLoop, or is there something else that you haven't shown us yet?

Are you thinking that there's some general strategy that we can just tell you that you can then apply that somehow avoids whatever difficulties you're having? If that's what you're asking for, it seems to me that you're on the right track--I can't think of some general strategy that's always superior to what you're doing. But again, if I knew more about your real context, maybe I could identify some particular opportunity.

"What is the best way?" is a very difficult question to answer. What are your objectives? Are you running into performance problems? Do you want to generalize? I really don't think there's any way to answer your question without a lot of guesswork.

As for feedback on your Mathematica code, I think your SolveInnerLoop function could be simplified to this:

SolveInnerLoop[S_, \[CapitalGamma]m_, \[Beta]_] :=
 Sum[Log[astar[s[[1, n, 1]], \[Beta], s[[1, n, 2]], \[CapitalGamma]m]], {n, 10}]