Read timed out errors are like a server crash in that players cannot join the server any longer, but it is still actually running as plugins will still do their functions, etc. Due to this, the server may still show up as online, but users simply cannot connect to it. This error will typically show up towards the end of the server log/console before all players are disconnected: "Read Timed Out".
In most cases, this error is caused by an out of date, incompatible, or buggy plugin. One plugin that is known to cause these errors is Permissions 3.x.
It is recommended to use an alternative permissions plugin that is actually up-to-date.
In most cases, a server restart will fix the issue. However, to prevent it from happening in the future, troubleshoot the server plugins. One basic method of troubleshooting is to simply remove plugins one at a time and let the server run for a while to see if it stops occurring. It is also recommended to update all plugins and remove any out-of-date plugins during this testing period.