Failure of your heteroskedasticity test can be regarded as indicating misspecification.  Have you done any other misspecification tests (e.g. autocorrelation, functional form, recursive residuals, etc.) and did any of these indicate misspecification?  Is your outlier the result of some policy change, innovation, change in method of compilation of your time series, or similar.  If so, you can use a point, or step dummy or another intervention variable to improve your model.   Even if you have heteroscedasticity your coefficient estimates are still consistent and you can use a robust estimate of their standard deviations.  What you do depends on your economic model, your data, and the aim of your analysis.

When Sven says 'whether that would be a proper "fix" '  I would think that he was referring to considerations such as the above.

John C Frain