It seems the functionality to mark builds as failed for "new errors" uses the total number of errors in the new result data, rather than the delta of errors.
Currently, if one of two errors is fixed, the build will be marked as failed with a new error threshold of 1.

Noticed with new error threshold of 1,
having 6 errors,
then checking in a new build with the result of 4 errors and 26 style warnings.
> [Cppcheck] Setting build status to FAILURE since total number of new errors exceeds the threshold value '1'.

Jenkins 1.554.1, CPPCheck plugin 1.16