I'm not too sure about the crashing problem, it could be old components going bad, capacitors failing are a major problem with A1200s, A600s and CD32s. Luckily they can be replaced pretty easily by someone with soldering skills.
To get your system copied, I have some suggestions for you to try if you'd like.
First, when you are copying these files, are you doing it from your full Workbench install, from a program like DOpus or something? If so, try booting without the Startup-Sequence and try copying everything either from the CLI or type LoadWB and copy it from a default Workbench. It's possible that some patch or other program you had running in the background may have been causing the crash.
Another suggestion is to pack your whole system into a LHA file rather than copying the whole lot of files and directories. This means you're only running one operation and creating one file instead of hundreds or thousands, so it may be a little safer and not trigger whatever caused it to crash before. It also has the advantage of having your whole system backed up to one file that is easier to transfer to some backup media like a CD or FAT-partitioned CF card which don't keep the metadata that Amiga filesystems add.