We have come across this same issue.
This was the permissions to certain Sharepoint lists that were used as seondary data connections, for drop down lists, in the form.
If your form connects on opening to these data connections, then all the people that use the form must have read access to those Sharepoint lists. Otherwise, they get prompted for their credentials to get access.
The issue occurred for us when someone had hanged the permissions on one of these lists to remove the access for various people, and suddenly the Form now asked them for "Enter your credentials to connect to ..."
Two solutions
1) - grant these people access to those lists
2) - In Infopath, only use that data connection when you KNOW that the user should have access to the list, based on a condition in your rule