You could try looking in Event Viewer to see if there are any errors there relating to Firefox.
When the problem occurs make a note of the time. Now Open Event viewer
To open Event Viewer right click My Computer and select Manage option.
In that window press the Plus against Event Viewer and select Application.
In the right hand pane is there any error showing in that log around the time the problem occurred.
If so double click on error. You will now get some details of the error post it here.
Alternatively you could try another browser to see if the error occurs in that browser.
If it occurs in another browser it could possibly be a Windows related problem not a browser problem.
Opera found here:
Opera Browser | Faster & safer Internet | Free Download
Or Google Chrome found here:
Google Chrome - Download a new browser
Are both good alternative options to test whether its browser or windows problem.
If you decide to try this.
Don't When asked allow them to become your default browser until your sure you want to.