I would guess that your issue has to do with the two variables under consideration having different amounts of missing data.
If neither has any missing data, and both are standardized to have mean zero and standard deviation one, then it is true that the regression coefficient should be equal to the pearson correlation.
BUT- if they have different amounts of missing data, the standardization could be throwing things off. The standardization is done with all available non-missing observations for a variable, but this may not be the same set of observations available for another variable. PROC CORR and PROG REG then analyze only those observations that are non-missing for BOTH variables, which could be a different set of observations used for the standardization of each variable.
I suggest you turn on the STD option on the MODEL statement on PROC REG to print standardized betas in the output. In a model with one predictor, the standardized beta should always equal the pearson correlation from PROC CORR.