As you wrote
instances of programs that are already running work without any problems
always keep a Konsole session opened.
And when KDE crash occurs, go to the Konsole and look for error messages in :
~/.xsession-errors (the '~' character stands for the home directory of the current logged in user, /home/<user name> )
Look at the end of the files for the last error messages.
Also what KDE version do you use ?
Is your installation well updated with all the last versions of packages ?
It's often suggested to rename the directory :
~/.kde (note the '.' character to point to a hidden directory)
and restart KDE to let it create a new .kde directory with default configuration files.
Try it and tell if this works for you.