Android loves to auto-disconnect you from any Wifi network that doesn't provide Internet. You need to go through a bunch of arcane settings to disable that feature.

This was my thought as well. I think the workaround is to have the device present itself as a captive portal type of thing, like you might encounter at a Starbucks, so that when the user is prompted to "Sign In" they immediately find the dead drop.

However I haven't actually played with this and don't know if that would work, or if the network would require DNS to function properly.