Hi!
Are you new to Knoppix? It appears that you are aware of system monitor, which means you must be aware of Linux and are conversant with it, although not too well.
Please don't be offended by my observations and suggestions.
Please do try to elaborate your situation for us members to help you - your computer info, other Operating System residing on your HDD, please provide as much information as you can.

GNU-Linux exists because of The Social Contract, and the FOSS architecture. In FOSS nothing is hidden except your personal data. You could even read the source codes, unlike the proprietary ones. Still, the system is robust. Even the System Admin doesn't know your password, but they can reset it.

Now given your problem, members would like to ask you about the application logs. If you aren't aware of the log files then members would tell you about their whereabouts, because the log files tell you why did the application failed
Iceweasel's history log is in ~/.mozilla/firefox/<some-random-string>.default/history.dat , similarly, for icedove, and system log, in /var/log.
Please don't forget to note if Iceweasel and Icedove freeze on a particular site or moment.
Someone will hopefully write to you more about solving your problem.
So please monitor when the two becomes zombie.
Someone must also have had the same problem, and maybe the solution is already present in the forum.