This was my second year in grad school and I was eligible (and received HM). he NSF wording is definitely confusing though. It says you must have no more than 1 year (12 months) of full-time graduate study. At the time of application, I only had to submit transcripts for the first year since fall courses were still in progress and technically not complete. This left me with only one year of study and eligible. Some faculty at my institution advised that you could be eligible if you had less than 24 grad credits at the time of application. So if students transferred in stuff from somewhere else or took extra courses it could hurt them, but one can always do the extra essay to make their case for eligibility.
So bottom line, do apply your second year. But we warned that they judge second years to a higher standard. Be sure to get more publications, conference presentations, and reseach experience, etc...