You are almost certainly using a lot more memory than you think.
It's not obvious what you have to do to see what your app is really using, but once you do it a couple times, you'll remember.
- Run with the Allocations performance tool.
- Click the VM Tracker "row" under "Allocations" (in the screenshot)
- Click "Snapshot Automatically"
Then you will see your Dirty memory (currently 20.34MB in my screenshot).
This should give you a much better picture of why your app is getting quit. You probably hav some large leaking happening.