Your issue is Java Security warning pop-up. There is no issue with the checkbox, and we need not expect it also.
So what we need here is to understand why browser give warning before running an applet? Is it because of security level?
If so, Follow the below steps:--
1. Go to Control panel
2. Click on java icon
3. Go to security Tab
4. What is your security level? Is it Medium? If so this will prompt browser to throw warning.
5. If so, make it High(minimum recommended)
6. I hope this should resolve your issue.
This may not help you with 7u55 and beyond.
We had some security dialogs popup without the "Do not show again..." checkbox. This only happened when the applet was launched from a server using SSL (https).
Caller-Allowable-Codebase: * https://*.<hostname>.com
and the checkbox appeared.