This is a long read but here's a link to the NLNAC 2008 Standards and Criteria for Associate Degree Programs in Nursing. http://www.nlnac.org/manuals/SC2008_ASSOCIATE.htm
The NLNAC is the organizational body that accredits ADN, Diploma, and LPN/LVN programs. It accredits some BSN and graduate programs but usually those programs are accredited by a different body (the CCNE).
You can also go to the site to see the lists of programs that were granted or denied initial or continuing accreditation or granted continuing accreditation with conditions or warnings. http://www.nlnac.org/Meetings%20&%20...un2010.htm#top
Usually a school has plenty of warning before it is denied accreditation. The most common reason for denial of accreditation is a high first-time NCLEX pass rate, which is one reason students see so many HESI or ATI tests during their programs.
When I was in my ADN program many years ago, there were rumors about a BSN program in the area being in danger of losing its accreditation because the NCLEX first-time pass rates were extremely low. Although the process was lengthy, the program did lose its accreditation in a couple of years and the school eventually shut down completely. Again, rumors had been flying about this school for quite some time before it lost its accreditation. So pay attention to what you hear. Do you hear rumors about your school either at school or in the clinical setting? Have graduates in more normal economic times have any trouble getting jobs? (Right now, don't take the fact that grads of your school might have trouble finding work as a grim sign---it's the economy---but if you hear that a hospital refuses to hire grads because they aren't happy with them, it's a bad sign.)
Finally, ask your advisor or one of your instructors about the accreditation process and where your school stands. I think this is a reasonable question and the school should be forthcoming as to whether or not it is accredited and seems solid.
ETA: if your school has excellent first-time pass rates on NCLEX, chances are that it won't have problems with accreditation.
Hope this helps!