re.match() looks at the begnning of the string for the match. Try using re.search() or re.findall() instead.
import re
pattern = r'(?<=TDY)[0-9][1-9]'
stringIn = '/XYZ01/TDY01/L01'
# using re.findall
print re.findall(pattern, stringIn)
# using re.search
search = re.search(pattern, stringIn)
if search:
print 'Found:', search.group()
else:
print 'Not found'
output:
['01']
Found: 01