I had this situation in RDSH environment.
Application would not connect to oracle database unless the user launching application had administrator rights, or administrator in another session had the application open at the time of regular users were trying to connect.
Solution to this is to grant the regular users "Create Global Objects" right via GPO or Local Security Policy.
To do this in GPO navigate to:
Local Policies->User Rights Assignment
Add the groups of users who need to use the application.