Agree, i have same bug.

yap, same happens to me, influence is smaller and was recalculated after two more turn.

didnt lose any resources, those were still in my border, even with the smaller influence radius...

It's here, too; when re-loading a save all my cities' influence radii get massively reset.  I've had wild improvements, previously built within my influence, up to 3 tiles outside my (large) capital city's influence upon re-load.  It's most noticeable with large cities, both mine and those of the AI.

This is a massive kick in the pants during play, of course, since all the wild improvements outside the reset radii wind up being demolished as soon as you hit the "next turn" button.

Strange behavior too.
Not sure if its tied to the radius of the cities actual buildings but it might.
Have some long-winded cities and if I'm not utterly mistaken after a second reload (thanks to 2 ooMs but they are better than in 109.e so no coplaints about smooth running...) the borders of my captial actually expanded.
Thanks to the first ooM in Midgame most of my cities are long snakes allready and Influence doesn't seem to shrink. So building cities in long strings might help. Still had the odd AI- and own-influence shrinks especially in conquered cities

(@Frogboy: AI sure loves to pack its cities tight. Another one for you to look into when writing the AI. Packed Cities are inferior in most cases even without this bug).

Might be one of the most annoying / obvious bugs but seems not so bad as some others in actual impact (save early game where it might be a neck-braker). Still warranting a quickfix imo lest new players be even more confused thanks to utter lack of documentation...

At least discourages reloading so it might actually get me of that bad habbit of loading often and loading early, so not all bad after all.