I have a gdb in the same folder. In AcCatalog I copied the feature class into it. I changed the code to point at it in the gdb instead of the mdb:
arcpy.MakeFeatureLayer_management('d:/swb/swb_data.gdb/precip_sites_yr', 'test')
And it runs without a problem.
I am only running it as a stand-alone script, saved as a python script, and executing it from Idle python editor. I need to do this to do other analyses outside of ArcMap. The full error message for the mdb printed above is below.
Traceback (most recent call last):
File "D:/code/python/layer_test.py", line 7, in <module>
arcpy.MakeFeatureLayer_management('D:/SWB/SWB_grid_builder_eq_area2.mdb/precip_sites_yr', 'test')
File "C:\ArcGIS\Desktop10.2\arcpy\arcpy\management.py", line 6043, in MakeFeatureLayer
raise e
ExecuteError: Failed to execute. Parameters are not valid.
ERROR 000732: Input Features: Dataset D:/SWB/SWB_grid_builder_eq_area2.mdb/precip_sites_yr does not exist or is not supported
Failed to execute (MakeFeatureLayer).
I have checked it over and over. The FC exists and is just fine. The script worked in 10.1.