Hmm, is the specifications of your server? Is it shared,VPS or dedicated?
What is your idle timeout set to?
What is this set to, (Pro) Auto-Delete Shouts Enter how long (in hours) before shouts are automatically deleted.
Do you have the shoutbox turned on for guests?
What is your refresh rate set to?
Try disabling other mods 1 at a time, then test shouts, and see if one of them is conflicting with the shout, I have seen this happen quite often.
It's likely just a case of having the options configured in a way your server is unable to handle =)
If you can give us that info we should be able to give you some settings to try changing to resolve it.