Hi Matthew - sounds like comes from the "waki o shimeru" (close your armpits) - this is a term often used in kendo - in closing your armpits, you're keeping your shoulders and elbows down, and not leaving an opening for anyone to take your balance.
I remember Prof. Goldsbury mentioning this term and it's usage in aikido at the Australian Winter School (Gold Coast) in July 2010 - perhaps he may have more information for you?
Well, we had a discussion about this in the dojo last night, after training. All the participants (all native Japanese except me) thought that it was a mistake, either for 隙がない (suki ga nai) or for another phrase entirely, such as 傍が甘え. (waki ga amae). This last phrase means that one's defences are weak and is clearly opposite in meaning to what is intended by the original phrase.