OK, there is this shop:
http://www.brusselsairport.be/en/pas...shopping/5253/
I emailed them and they do sell BASE. However it's a dedicated mobile rental shop, not convenience store.
You may have gotten it at a Relay shop, which is also listed as being at BRU.
I emailed Rent2Connect and they claim activation is instant so I'm a bit concerned about trying out a BASE card if it takes that long to activate.