Varimax rotation is used when you believe that the components are not correlated with each other (Varimax constrains correlations between components to 0). An Oblimin rotation will allow for components to have a non-zero correlation. For research in social sciences, it might be a good idea to use an oblimin rotation first and inspect the correlations between components. If they are low, then using a varimax rotation is more empirically defensible. 

I agree with Daniel that we are more likely to have correlated factor in the social sciences, so I would also recommend starting with that, and only use an orthogonal rotation (i.e., uncorrelated factors) if the Oblimin says that is justified. That means examining the matrix of correlations among the factors to see if any of them are larger than .3 (an arbitrary cut-off).

Maximum iterations for convergence is basically an internal aspect of the factor analysis process which is very unlikely to have any impact on the estimation of your results. If you ever get a message indicating that there was a "failure reach convergence," then you would specify a higher number of iterations than the default, but again, this is very unlikely

Basically agree with the two prior answers. However, don't assume social science research would NOT want to try to find orthogonal components. For example, in some urban research (look up factorial ecology) there was a finding that the three main principal components might have an interpretation in terms of "independent" factors. The loadings of the underlying variables on the components give a clue to a good interpretation.  Recall that the individual observational units scores on these components might then be mapped to give different uncorrelated aspects of the spatial pattern. In the end though, PCA  with correlated (VARIMAX) might be more realistic in that it is probably impossible to separate socioeconomic data cleanly into non correlated dimensions (e.g.  home ownership,  income, and educational patterns have co-variations in US cities).

Thank you all for your very useful responses. I am grateful. 

what is meant by iterations????

Thank you very much sir...! I also learnt from this discussion.

I learnt alot from this insight, Please, can i be clarified whether PCA can directly be used to test a hypothesis and significant inferences made

at Spss, default is 25 "maximum iterations for convergence" 

I have 116*181 matrix, failed with 25 "iterations for convergence" but when I change it to100, The "failled" does not appear. Rotation was conducted.

Could this be acceptable?

I have 54*54 matrix, failed with 25 "iterations for convergence" but when I change it to50, The "failled" does not appear. Rotation was conducted

Thank you all for your very useful responses.

I also have the same problem and I am still searching the guide to put how many iteration and the reason why we need to increase iteration. and also why iteration affect rotation?

Thsnk you for helping us understand these concepts

Thanks a lot for all the useful info.