Sharepoint 2010 Error "You do not have permissions to access a database

First make sure the user has sufficient permission to access the database/web service.

Next, in infopath ->Tools ->Form Options ->Security and trust ->Uncheck “Automatically determine security level” (If database/webservice is on same domain then select domain else select proper option)

Now Convert your data connection in udcx file:

* For this, create a data connection library in MOSS
* Now open infopath form -> tools->Data connections
* Select data connection and click on “Convert… “ button
* Give the data connection library url with file name.
* Open Data Connection Library and Right click on udcx file -> "Approve/Reject" -> Select Approve and click OK.

Goto Central Administration ->Application Management->configure infopath form services-> and ensure the “Allow user form templates to use authentication information contained in data connection files” is checked.

If your database/web service is placed on another domain then you need to check next option “Allow cross-domain data access for user form templates that use connection settings in a data connection file”.

Source:social.msdn.microsoft.com