Actually, they can stop working; there is even a name for it: tachyphylaxis.

http://www.mayoclinic.com/health/ant...ssants/AN01312

http://www.johnshopkinshealthalerts....ty_3288-1.html

http://www.ncbi.nlm.nih.gov/pubmed/18694599

I have had to switch antidepressants several times due to this problem. It's hard to know why it happens, but in a few patients this can be a problem. Generally, switching to a different AD has corrected the problem quite well.