This is a fault of the software and ultimately must be resolved by the software company. However, you should be able to tweak the system so that an ordinary user can run the software. Usually, the reason the user needs elevated privileges is that the software is accessing or making changes to files, folders or registry keys that an ordinary user does not have the access to, but a Power User or Administrator does.
So to solve the problem, create a special group. Find the keys, files and folders that the user needs access to and give the group the access. Put the user's account in that group. To find the files/folders/keys, use auditing to find those denied access. Another possibility is to use the programs filemon and regmon. These utilities available from www.sysinternals.com can be run before running the program and will trace the usage of files or registry keys.