This is unrelated to Infopath and even Sharepoint, it is for any web apps.
As a user I can assure this by
enter "Internet Options" (either through Internet Explorer menu Tools or Control Panel) > Security > Local Intranet > check "Automatically detect intranet options" > Advanced options >> Add your sharepoint weapps using wild cards
The short NETBIOS names also should be enlisted
I have added sharepoint online sites to list of "Trusted Sites" and "Trusted Sites" with "Local Intrenet" set to the Low security zone
As a system administrator you probably want to apply this to all users
Login to DC through account with domain admin privileges and create a package with above settings
Control panel > Add or remove programs > Add/Remove Windows Components > Internet Explorer Enhanced Security Configuration > Uncheck the Internet Explorer Enhanced Security Configuration > Next, etc. to complete wizard
Start > All Programs > Administrative Tools > Active Directory Users and Computers > righ-click your domain name (or organizational unit to users of which you want to apply this) > Properties > "Group Policy" tab > New > enter name for the new Group Policy Object > selct it > click Edit button> User Configuration > Windows Components > Internet Explorer Maintenance > Security > Security Zones and Content Ratings > Import the current security zones and privacy settings > close all opened windows
Optional: Re-enable Internet Explorer Enhanced and Security Configuration < Add/Remove Windows Components
This changes can take time to propagate up to 90 min
Therer are other variants but it is not in any way a topic on Infopath (or even Sharepoint)