By default (I mean in Default.nb style sheet) the Section style resets the subsection counter and many others, by means of the following option:
CounterAssignments->{{"Subsection", 0},{"Subsubsection", 0}, {"Item", 0}, {"Subitem", 0}, {
"Subsubitem", 0}, {"ItemNumbered", 0}, {"SubitemNumbered", 0}, {"SubsubitemNumbered", 0}}
So, if you want some of such headings not to re-start the counter after a section, just do the following:
Open the notebook's style sheet and add a Section style and then use the option
CounterAssignments->{{"Subsection", 0},{"Subsubsection", 0}, {"Item", 0}, {"Subitem", 0}, {
"Subsubitem", 0}, {"ItemNumbered", 0}, {"SubitemNumbered", 0}, {"SubsubitemNumbered", 0}}
adding or removing the counters you want to modify (add a counter to reset after each Section, remove from the list to not reset).
In our case, you should remove the {"Subsection", 0} from the list.
Here is a picture of what you should get.