Normalization in production
Really depends

Why? updating everything in production (pre-processing, fitting etc) can get extremely expensive. If you have some complex architecture it is not worth it.

Alternatives


Approximate covariate shift if you know distribution of your future data you can adjust all your, for example normalisation parameters, in advance.
Save your you future data every time you make prediction, it could be cheaper to quickly save your data in DB and depending on your system do updates weekly,monthly