OK, timeouts, do the log say something like “a tick took longer than x seconds and are considered frozen. Stopping server”?
If this is the issue there is a setting in server.properties you can adjust to allow for longer ticks. I have to have long ticks, or else my servers stop periodically:
in server.properties:
max-tick-time
give that one a higher number, I run mine at 120000.
As for Minecraft Server memory:
You adjust that byr increasing or decreasing Xmx and Xms. I make sure that the Xmx total off all my Minecraft servers equals or is lower than my physical memory, and I allways set Xms at half what I set the Xmx to.
If you only run one server, its probably not memory that is your biggest problem, since a small server should run fine on half a gig of memory. Try to adjust max-tick-time first.