A baseline consideration for how interesting this might be is to imagine that inflation is a random coin flip (obviously, it’s not, although if you’re measuring it to hundredths of a percent, it might kinda behave that way a lot). If it were, you should expect a string of 7 months of increasing inflation in a row to happen 1 in 2^6 of the time, or 1 in 64 7-month strings. If you further restrict it to having all 7 of those months in the same calendar year (as opposed to a string that straddles more than one), then you only have 5 possible starting months per year, so you should expect to see such a string slightly less often than once a decade.
So, it happening just once in a ~45 year span strikes me as: a slight outlier, but not that interesting.
A more sophisticated model of the inflation rate might make it more interesting, but probably not. For example, the ways in which inflation is not like a coinflip make it tend to revert to a mean (both because noise in the measurement is random and because policy changes take place when it strays too far from what the central bankers want it to be), which makes the actual likelihood a bit less often.
Also, realize that you’re looking at a specific pattern and noticing something (apparently) interesting about it. If you saw a different pattern, you might think that pattern was interesting. Like, you could just as easily noticed that, say, inflation alternated increasing and decreasing in every year in 1987, and that didn’t happen in any other year since the 1930s (I made that up, don’t go looking for it). Which is true (it’s not) but so what? If you look at enough random noisy data you’ll see lots of things that aren’t interesting.