I find typical issue of overlapping for polygon buffering at times it fails.
Problem can be solved by splitting them into different polygons for which tools are available and combining later, but why at all it should fail. It amazed me such trivial thing can be bothering.
many reason... file too large... complex geometry... unprojected data (not ideal)... dissolving overlaps for the aforementioned..
straight failures are usually the result of poor path names for the source and/or destination
Details and examples would be of interest to us and to the developers should this be a persistent problem with your workflow.
Yes, the way around through modeler where each polygon was separated to create buffer around each polygon (protected area) of monument was partial success, but it also failed due to paucity of memory when run in batch mode. While I agree with first one i.e. file too large, I am curious to learn why complex geometry should fail the process where as option for dissolve is "None". There are not many entities hardly 50 overlapping buffer
I occasionally find that small errors in the geometry can cause some of the geoprocessing tools to fail, particularly in large data sets. I may be stating the obvious, but have you tried running the Repair Geometry geoprocessing tool before buffering?
Besides geometry errors (which should be checked as a matter of procedure), consider a polygon with multiple holes/donuts and a concave convoluted shape... buffer such features may necessitate the removal of a portion or all of some of the geometry elements (ie the holes). If overlaps are involved, this can cause issues, although you indicate that the geometries were kept separate and not dissolved.