first tell us which version of windows and what antivirus program did you have prior to installing the Norton suite? Did you fully remove it using the dedicated removal tool from the company or just use add remove programs?
If you have the Norton suite it likely has a built in firewall is your windows firewall turned off, it should be if you have the Norton one active.

when in relation to this did you get the firefox version 5 update?

I have Windows Vista version 6.0. Before Norton I had McAfee. I just used add/remove programs, I didn't even know there was a removal tool from the company (embarrassed). If that is the problem is there a way to go back and remove it now? I don't know if the Windows firewall is turned off or not. I had Firefox 5 update several months before downloading Norton suite.

you should go ahead and use the dedicated McAfee removal tool, and or app remover, because McAfee is horrible about leaving lots of stuff behind, I had it at one time and went through a long removal process that I found on their forums, you can find a link to the removal tool here and also a link to a tool that can help you to remove it.
Antivirus Product Removal Tools
Using AppRemover
AppRemover

that will be your best bet for a full removal

to determine if your windows firewall is on or not go to your control panel and the security area there you will find the firewall and can see if it is on or not. If you are running the firewall in the Norton suite then you should not have any other firewall turned on. If your Norton does not have a firewall then you would want to have the windows one turned on.

after you do that let us know if you are still seeing the same thing happening.
I do not use Norton so am not familiar on how to adjust the scanning schedule and properties maybe someone else knows.

Thank you so much for the help Ravencajun. I will definitely do those things :)

To fix this problem, you need to Open Norton, then open the Utilities, click on clean your disk, click on the browsers tab, and click on Firefox. Take the check mark out of passwords, and then click on save. You should now be able to keep your passwords in Firefox. You might want to do the same for IE, just in case you need to use it, and/or any other browser you have installed. Good Luck