Read timed out errors are like a server crash in that you cannot join your server any longer, but it is still actually running (plugins will still do their functions, etc). Due to this, your server may still show up as online, but you simply cannot connect to it. This error will typically show up towards the end of your server log/console before all players are disconnected (it will usually be just one line saying "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 In most cases, this error is caused by an out of date, incompatible, or buggy plugin.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 so it is recommended to use an alternative permissions plugin that is actually up to date (this goes for any plugin).
In most cases, a server restart will fix the issue. However, to prevent it from happening in the future, you will have to troubleshoot your plugins. One basic method of troubleshooting is to simply remove plugins one at a time (or in groups) and let the server run for a while and see if it stops occuring. It is also recommended to update all plugins and remove any out of date plugins during this testing period.