SAS proc reg/spec - Why are binary predictors flagged for singular matrix?

Hello all -

I am building a simple linear regression model (OLS) with both continuous and binary independent variables paired with a continuous dependent variable. All binary variables are dummy coded as 0/1. I am using the SPEC option of PROC REG in SAS/STAT 9.2 to run the White test for heteroscedasticity.

The strange thing is that when the model includes any binary variable, I get an error message that the average covariance matrix is singular, making for unreliable variance estimates. But the actual test itself (first and second moment specification) is fine in all cases.

I have tried various combinations of predictors in the model and noticed that I get this message always, and only, in the presence of at least one binary predictor. With only the continuous predictors everything is fine.

I suspect that this is something mechanical about the White test, not about my data in particular. Let's assume a simple model with the continuous dependent and one binary independent variable, dummy coded. Could that be flagged as a singular matrix just because the variance matrix has, in effect, only one cell?

Please note:
1. There are no other signs of heteroscedasticity. Scatterplots look fine to the naked eye. When I directly test for differences in variance, nothing is significant.
2. I have tried transforming the dependent variable in a number of ways to see if that would help, though I was skeptical. The boxcox function gave me a lambda of 1.25. As I suspected, that transformation didn't resolve it.
2. My sample size is not likely a problem (about 400).
3. The data is otherwise unremarkable. No outliers, no other diagnostics are being flagged.
4. I have looked elsewhere on the web and have searched this forum, with no luck.

Thanks so much. This is the first time I've posted here.