Which version of LW are you using?
Sorry I don't have any immediate answers. The only time I've seen or heard of such as thing was some years back on a different OS. I'd hide the program but sometimes it would refuse to show again. But that was due to a much earlier version of Java.

When you say LW disappears ... do you mean the interface simply disappears or the program stops running & quits?

Do a control-alt-del & bring up task manager & see if Limewire is still listed as running when it disappears.

Is LW the only program it happens to?

Do you use an anti-spyware program or similar, & if yes which one(s)?

Did you give LW full clearance thru your firewall if you have one? Is there a port opened on your modem/router for incoming?

What graphic card brand & model are you using?