Go and check your memory situation at "about this computer..." under the Apple-mark on the left top of your screen. If LW is eating more than 60 MB, and you've only about 2 to 3 MB left available (regardless of how much you're supposed to have left), then this is a well-known-yet-never-solved-memory problem.
I know little about technical things (someone has explained about this program being Java based and so on being the cause of this problem), but what worked for me was a "down-grade" to LW 2.1. I downloaded this version (quite appropriately) from Limewire (someone was sharing it)! All versions later than 2.1 seem to have this problem (I don't know about those who are using OS X). But for someone like me (OS 9.1; G4/400, 128 MB RAM), down-grading to 2.1 did the trick.
Some suggested to add more memory on to your RAM, but from what I hear, this doesn't always help.
It's a pity to see that the earlier version works more stable than the later ones. I have little faith in the current version. I will up-grade when ("IF") someone makes an official notice saying that the "memory problem" has been solved for ever!

Happy sharing.