As I said, if you look at the errors the code will output, you should see it says:
"Output dataset already exists" as part of your
except:
print arcpy.GetMessages()
As you have the try, except outside the loop, what happens is:
Clip 1st layer
Export first layer to CAD
Clip 2nd layer
Crash as output New.DWG already exists (You have this message being printed..)
Then, it exits the try except loop so stops processing.
Here I have given each CAD a unique name, and moved the try except so that it does not stop ALL processing when it crashes. (Just skip the current dataset)
arcpy.env.workspace = arcpy.GetParameterAsText(0)
obszar = arcpy.GetParameterAsText(1)
out = arcpy.GetParameterAsText(2)
datasetList = arcpy.ListFeatureClasses()
index = 0
for dataset in datasetList:
index +=1
featureClassName = arcpy.ValidateTableName(dataset, out)
outFeatureClass = os.path.join(out, featureClassName)
if dataset != os.path.basename(obszar):
try:
arcpy.Clip_analysis(dataset, obszar, outFeatureClass, "")
output_CAD_name = 'CAD_' + str(index) + '_New.Dwg'
arcpy.ExportCAD_conversion(outFeatureClass, "DWG_R2010", output_CAD_name)
except:
print arcpy.GetMessages()