The small cog is susceptible to too little cable slack but not to too much cable slack, assuming the limit screw is set correctly. You should also consider cassette wear. The 12-tooth cog will wear noticably faster than the other cogs, because it is smaller and goes around faster. If you've got more than 1000 miles on this cassette, there is potential for this kind of wear.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72