I ran a fairly large bifactor model (40 items loading on 7 factors) on ordinal scales (7-point scale). Here is the problem. When I specified residual terms to be uncorrelated (i.e., the residual covariance matrix is diagonal), estimation of this model didn't converge. However, if I specified one (and only one) pair of items to be correlated, the model converges rapidly.
What could be the possible causes that are associated with this issue? Any thoughts will be enormously appreciated. Thank you.