I am struggling with frequent database errors with one of my none business sites and it's driving me nuts. They resolve fast-within a refresh, but the company says that nothing is wrong.

Tell me I'm not crazy. For me to be getting errors at least four or five times a day, something has to be wrong, right?

More information would be needed to give an opinion.
What type of server are you on?
What script is getting the database errors? What version of the script?
How much traffic to the site?
Which version of PHP? If it is a php script causing the errors.
Which version of mySQL is the server using? Assuming this is a mySQL database.

How about what is the error??

which script you are getting error on? send more info

Obviously one need more information. if you cant copy paste the actual mysql error message or dont know what the error is, obviously you are being silly.

My assumption is the database server is overloaded and you are getting a maximum connections exceeded error. This needs to be verified.

I am not being silly. There are not enough visitors for this to be a problem of too many visitors.

The error is simply this;

Database Error
Please try again. If you come back to this error screen, report the error to an administrator.

Don't really tell me much, don't see how it tells anyone else much either

I don't think anyone is accusing you of being silly but you cannot expect any help if you don't at least address some of the questions asked here.