Confused here... if possible can you provide the exact steps?
From what I read in the title and your message you open FF, then go to your web page and now you want to minimize it, right? So, if CNN.COM is you home page and you start FF, it opens to CNN, then what do you do? Hit the - on the upper right to minimize FF? OK, assuming this is the case, two things to try. Use a different URL and then minimize. Does it also disappear? If so, you've got an FF problem.
If it is a FF problem, you need to start it in SAFEMODE which takes all the extensions and themes out of the equation, they may be causing the problem.
If ONLY your specific home page is the problem, it still could be an Extension or theme problem as well. Do the same, start in SAFEMODE and see if it works.
Check HERE for instructions on starting in Safe Mode.