I found that if I un-check the Store Output and Store Error boxes that I had better luck with the variable setting. This may be coincidental. I see that now in the Variable's Value that the code for the task is sitting in there and it seems to be storing now.
Steps performed for tesitng, and now the variable is storing:
1) Uncheck Store Outpur
2) Uncheck Store Errors
3) Create task to Remove Variable
4) Run job - SQL sets output
5) Variable task sets the value to the output of the SQL
6) Send mail using the variable.
drandles attached the following image(s):