Dear Statalist experts

I am running an IV regression with a dummy dependent variable and primary school fixed effects in Stata 16. The regression has the form: ivregress 2sls y (endogenousvar = instrumentalvar) $controls i.primaryschool, first cluster(primaryschool). I get the error Warning: variance matrix is non symmetric or highly singular. I tried to run the regressions with vce(robust), with cluster(primaryschool) and without specifying the standard errors but I always get the same error. Reading an older post in statalist I understood that the cause of the problem might be because of having many primary schools where only one observation attends. When I run the non-IV version of the same regression though I do not have this problem and the regression is run as normal. It is really important for my model to use both the IV and the fixed effects, any suggestion on how I can overcome this will be really appreciated.

Thanks a lot in advance
Konstantina