Apparently a '-' at the beginning of the command means "run this thing and if it fails ignore the failure and keep going".  I tried to add an if/else in the build target to use the '-' with the selected builder was "suspicious" but I couldn't make it work, so I ended up adding a new build-and-continue that uses the '-'.

make linkcheck and make doctest had the same problem, so I fixed them too.

The output now looks like this:

$ make suspicious
mkdir -p build/suspicious build/doctrees
python tools/sphinx-build.py -b suspicious -d build/doctrees -D latex_paper_size=  . build/suspicious 
Running Sphinx v1.0.7
loading pickled environment... done
loading ignore rules... done, 359 rules loaded
building [suspicious]: targets for 428 source files that are out of date
updating environment: 0 added, 0 changed, 0 removed
looking for now-outdated files... none found
preparing documents... done
writing output... [ 81%] library/unittest
WARNING: [library/unittest:19] ":port" found in "host:port"
writing output... [100%] whatsnew/index
build finished with problems, 1 warning.
make: [build-and-continue] Error 1 (ignored)

Suspicious check complete; look for any errors in the above output or in build/suspicious/suspicious.csv.  If all issues are false positives, append that file to tools/sphinxext/susp-ignored.csv.