OK that's odd - I opened the app up this morning and got an 'Access is denied' (Which is possibly one of the first times I've been excited to see a message like this).
I opened without data to put entries back in section access table. Works. Then tried to remove them again and once again have full viewing access with:
ACCESS, USERID, %AUTID, OMIT
USER, DOMAIN\ME, ,
At a guess it appears to be some sort of caching issue (maybe). Tried different browsers (IE11 & Chrome), so at a bit of a loss again.
For anyone else that looks into this thread that experiences this:
I have found a workaround - between each alteration of the Section Access you need to completely close all instances of the app on your PC (includes cross browser), and open the app again. I've been completely closing all qlik sense tabs between changes, but I would expect that you can get away with just closing the app in question.