If your server stops by itself and the console mentions out of memory, or the exit code 137, it ran out of RAM and was shut down.

Is it really out of memory?

High memory use alone is normal. Java keeps memory it may reuse. Read Understand RAM Usage before panicking. You only have a problem if the server crashes or lags heavily.

Fixes

1. Reduce load. Lower view-distance and simulation-distance, see Common server.properties Settings. Cut mob limits, see Mob Spawn Limits.
2. Find the heavy part. Use Spark to see what uses memory. Remove or update any heavy plugin or mod.
3. Watch for leaks. If memory slowly climbs until a crash, a plugin or mod may be leaking. Remove recent additions to find it, see Binary Search.
4. Check startup settings. If your Startup page has a memory setting, leave some room for the system, roughly 85 to 95 percent of your plan’s RAM.
5. Upgrade. Large modpacks and busy servers need more RAM. See Choosing a Plan and Upgrades and Downgrades.

Need help? Open a support ticket.