when inflation comes, why doesn't the expectation of that inflation lead to proportional increases in nominal interest rates, thus keeping the real rate constant?
The question seems ill-posed.
Saying "when inflation comes" makes it sound like it just happens to appear, like that poem about the fog rolling in on little cat feet.
Inflation comes from bad monetary policy, which in turns usually comes from bad fiscal policy. So what we are talking about is expectations about policy regimes and changes thereto.
Inflation (or a change in policy regime) could affect real interest rates either when it is expected or when it is unexpected.
(1) Should there be any response of the real interest rate to expected changes in the policy regime?
(2) Should expectational errors tend to be high when inflation is high, and conversely?
Perhaps the answer to both is "yes."
Suppose that the interest rate on 10-year Treasuries is 5 percent but everyone expects the Fed to raise the money supply at an annual rate of 6 percent over the next 10 years. What can I do? I can try to stay away from holding long-term nominal bonds. If I am aggressive, I can go out and take out large long-term loans, until I am charged an exorbitant risk premium. But what hard assets do I buy? Gold? Real estate? Stocks? Bonds denominated in foreign currencies? The uncertainty over how to make the inflation bet makes it difficult. So I might be relatively cautious, which could mean that bond prices stay a bit higher than they should, and real interest rates decline a bit.
In the other direction, if we think that monetary growth is headed to 1 percent or lower over the next 10 years, then my inclination is to pay off my debts and load up on Treasuries, so that I can get a nifty real return by merely clipping coupons. But do I completely ignore hard assets? What if my forecast turns out to be wrong? Or what if stocks do even better than bonds in this low-inflation environment? So maybe bond prices don't fall as much as they should, and the real interest rate goes up.
The second issue is this: what should be the relationship between expected changes in the policy regime and actual changes in the policy regime? If we are using past data and regression models to predict future money growth, then we should predict less variation than actually takes place. As a result, when realized money growth is high, expectations will be below actual, and conversely. Thus, the realized real interest rate will tend to be a bit low when inflation turns out to be above-normal, and conversely.
As an aside, I don't think that the behavior of real interest rates is invariant with respect to financial innovation. I doubt that an empirical study of interest rate behavior in the 1970's and the 1980's has much relevance today.