Thanks for posting your question. We have seen quite a few questions from parents considering grade retention for their child recently, so I know that there are a lot of parents who are struggling with a very similar decision. You are not alone.  
 
As you think about grade retention for your daughter, there are a number of issues to keep in mind. First, you should learn all that you can about research examining the short- and long-term effects of grade retention. The National Association of School Psychologists (NASP) has published a position statement (which means that prominent members of the NASP got together, reviewed the evidence, and determined their official "position" on the issue) on grade retention. Dr. Jimerson at UCSB has also conducted a great deal of research in this area, and he has suggested that more comprehensive interventions should be considered rather than simply retaining a child. Overall, the research indicates that students who are held back/retained have worse outcomes academically and emotionally than their peers who were also candidates for retention, but who were promoted. For more on this, see links below.  
 
You didn't mention whether your daughter is struggling academically or not, but given that her teacher's largest concerns center upon social issues, I wonder if the best course of action would be to promote your daughter to fourth grade and begin a social skills intervention during the summer, continuing through the next school year. Your daughter's teacher or school counselor will most likely have recommendations for local community mental health agencies that provide social skills groups for children your daughter's age. Social skills groups are generally taught by a mental health professional and children are led through a series of exercises, including role-playing that allow them to get feedback about their social skills and develop new, more adaptive ones. Most community mental health agencies offer services on a slide-fee scale (you pay only what you can afford) or some kind of scholarship.  
 
Whether these kinds of groups are available in your community or not, you should also check with your daughter's school to see if they have similar groups. Most schools offer groups like this to help children with your daughter's very same difficulties.   Thus, the final decision is yours, but the research on grade retention is not that positive for children who are held back. Rather, most experts recommend specific, targeted interventions to manage the child's areas of relative weakness.
 
Hope that helps. Let us know if you have any additional questions!  
 
L. Compian, Ph.D.
Counseling Psychologist
Education.com