Hi, welcome to TSF
You'll probably find that Firefox is actually using 206,000K (approx 200MB, 20% of your total RAM).
Reboot the computer, then hit Ctrl-Alt-Del to bring up the Task Manager and click the Performance tab at the top. Make a note of the Total Physical Memory and Total Commit Charge when you first turn the computer on, and again when Firefox starts misbehaving. Post back with both sets of figures.
How many Firefox addons are running?
Have you tried clearing the cache? Tools > Clear Recent History, click the Details button, select 'Browsing & Download History' and 'Cache', then click the Clear Now button.
I've also been using Firefox on a 1GB Asus Eee XP netbook since December, but haven't had any problems with it so far (usually 5-10 tabs open). To get round the 1GB RAM restriction, I've installed a 4GB SD card into the slot on the right-hand side of the keyboard, and installed eBoostr
which acts like ReadyBoost that is found in Vista and Windows 7. Programs start and run much quicker now. Might be worth looking into if you find 1GB RAM is going to be a problem when multitasking or browsing with several Firefox tabs open.