I saw this  today (on global interest rates) and decided to look at what the old model shows for real interest rates in the US where we take 1 + i = (1 + r)(1 + π) where r is the real interest rate, i is the nominal interest rate and π is the inflation rate. Here's the fit to the price level and the 10-year interest rate:
And here is the resulting real interest rate:
The downward trend since the 1980s appears here as well. If this model is successfully describing that trend, then we can trace it to the diminishing impact of changes in the monetary base on the price level. In fact the global data in the link  above seems to imply that this diminishing impact is widespread, implying many developed countries are moving towards the right on this diagram:
The diminshing impact of monetary expansion shows up as a negative (downward) curvature as you move to the right on the graph.