How do you automatically split all loop links in a table with line objects? A loop being one where first and last coordinate is the same. Should be split at 50%.
Here is a ModelBuilder approach that works:
This creates a new feature class with just the closed polylines, split at their midpoint. Up to you whether you can use that or need to go further to update your original feature class in-place. Note that the tools involved require an ArcInfo level license.
Here's how it works:
Aka a linear ring - the precursor of a polygon... but HOW you want to split them still requires a bit more information. You say 50% but this, in itself is still a little vague. Do you mean half the enclosed area, half the length of the linear ring or must the split fall diametrically opposite the start/end coordinate? Does the orientation of the rings matter? Are the rings simple regular shapes?
Anyway, I will take a stab at this and assume that, by 50%, you simply mean half the length of the ring. If you don't need to make this a btach process, ESRI has a tool for this and an explaination here: http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/into_an_equal_number_of_parts/001t000003vz000000/. In your case the number of parts should be set to 2, obviously.
Alternatively, a more complex approach, but one that lends itself to automation would be to use linear referencing: Make your data M-aware, iterate over the lines, get each line's length and set an M-value at the mid point, Finally split the lines based on their M-Values.