@dori, consider everything @dalacor said concerning the reliability of USB flash drives. That said, however, there really should not be any reason you cannot run Manager from one. Once you open the application, it will be on your computer in RAM. The application itself is fairly small by modern standards.
The issue will be poor performance, because data transfer speeds to/from the USB drive will be quite slow compared to the local bus. No data is stored in the application. All data is in the application data folder that @sulfuror mentioned. Constant access is required for good performance. Performance will be governed by where your data file is, not where the application is.
There is never a worry about losing Manager. You can always download a new copy from the web site. The issue is safety of your data, which is why backup files should never be on your computer and should be made frequently. Never allow more time between backups than you are willing to re-enter all the data.