The central issue is that these "robust" standard errors are derived to deal with heteroskedasticity. If your $\epsilon_i$ in regression do not have a common variance, there is no point in defining an estimate of $\sigma^2$, as there is no population analogue for it, and the sum of squared residuals, central to definition of both $R^2$ and the standardized coefficients, does not make much sense, either. For sure, there is no longer an $F$-distribution to be used in tests on reduction on the sum of squares. My guess is that SPSS duplicates Stata's behavior on this; Stata has had it for what, 20 years? This FAQ is written by the author of Stata's
robust standard errors in 1998 when they had it up and running for a couple of releases; this and some other FAQs concerning robust standard errors are worth looking at.
Disclaimer: I don't like the term "robust standard errors" very much. If at all. I positively hate it. There is no single unique definition of "robust" standard errors; rather, there is a whole class of these standard errors, and you can always find something wrong with any member of the class. White/Eicker standard errors are consistent under heteroskedasticity, but are biased in small samples even under homoskedasticity, and inconsistent under serial correlation or clustering. Newey-West standard errors correct for autocorrelation, but only up to a certain lag. Any of these standard errors are not robust in the Swiss meaning of the word: outliers going to infinity still screw them up. I think economists tend to use more cautious ``heteroskedasticity-consistent'' terminology.