Assuming your partition is big enough you're not doing anything wrong.

The problem is the N900's watchdog*, which is supposed to reboot your phone if some process stops responding. Whenever you put the N900's CPU on full load for more than (say) 10 minutes (which can easily be done by file system I/O) you'll likely trigger its reboot routine.
You can alleviate that problem by running every program that's likely to trigger the watchdog with a lower nice priority:Unfortunately that doesn't solve the problem because even if your program has a low priority (and therefore the watchdog will be served first) due to a high load caused by your program it might take too long to free the memory that the watchdog requires and the device will still reboot.

The only safe way to avoid the watchdog being triggered is to make sure the N900 won't be on full load for too long. So in your case it should help to not copy everything at once but to copy one (or some) directory at a time, wait until the load is down to normal again and then start the next one.

*) rant: In my opinion from a technical/hardware point of view the watchdog is the biggest flaw in the N900's design. I've had numerous reboots due to the watchdog, none of them being justified. There was no runaway process, I just wanted to do some task that did not finish within a few minutes (dist-upgrade Easy Debian, compile something, etc.).
So if someone has found a way to disable the watchdog completely (without putting the N900 in R&D mode) I'd be grateful to hear that!


@Estel:
While we're at ranting, I totally agree with your browser rant. Unfortunately text browsers like lynx or w3m don't work that great on the N900, but you might want to try chimera2 [1] in Easy Debian or dillo3 [2] once I've managed to dist-upgrade to Wheezy (which I can't do on the N900 due to the watchdog, therefore I've started to tinker with qemu on my PC).
Afair there was a "dillo3 on Maemo" thread some time ago (it might as well have been a youtube video I stumbled upon). Both browsers are severely limited in their functionality, but for simple browsing they should suffice.
There are also midori [3] and arora [4], which might be alternatives. They are supposed to be lightweight, but according to my experience that highly depends on your system and I haven't found out yet why that varies so much.

[1] http://packages.debian.org/squeeze/chimera2
[2] http://packages.debian.org/wheezy/dillo
[3] http://packages.debian.org/squeeze/midori
[4] http://packages.debian.org/squeeze/arora