Happens pretty frequently to me too. Usually it's with large selections. Saving seems to still work, so sometimes I have luck saving back to an MUS and reloading it after clearing or restarting Mike Urban. Another work around I use pretty frequently is to just work with the feature sets in ArcGIS instead as it's selection capabilities are more robust.
I haven't had any luck with that, as I don't believe ESRI supports side-by-side instances of ArcGIS but this article may help if you only have one computer and really want it to be installed simultaneously:
I don't know anything about catchments, but MUS files are selection sets. You make them by selecting elements in Mike Urban then clicking the Save Selection button (right side of the Selection toolbar or using the menus Tools > Selection > Save Select). (It's just a text file of MUIDs prefaced with the element type; you can check it out by opening up one in a text editor after creating one).
You probably already tried this, but doesn't work to put in a relative folder path in the output scenario ID dialog box, like you can with various support files like hotstarts and dsf0 files. If you really wanted to do it, you could probably use something third party - the easiest way I could think of would be to write an Autohotkey script to monitor the folder and move any PRF files based on the file name to a subfolder.
Anyone know of a way to get the mup file to use relative paths for the reference layers? Similar to ArcMap's File > Map Document Properties > Store Relative Paths to Data Sources option. Didn't see anything in the help file or manual. Working around it now by using a relative path'd lyr file, but that's a little cumbersome. Looked inside the xml of the mup, but the paths are all inside the encrypted text.