We usually do... but I just looked it up and wow, it doesn't have to be refrigerated ever!

<< Where should TABASCO Sauce be stored?

TABASCO Sauce should be stored in a cool place away from direct light, such as a cupboard, pantry or cabinet. It doesn’t have to be refrigerated after opening. Once a bottle of sauce is opened, the color may change, but the product won’t spoil. Refrigeration almost always helps to slow this process but isn’t required. >>

http://www.tabasco.com/mcilhenny-company/faqs-archives/#where-should-tabasco-be-stored

So I guess refrigeration helps slow the rate of color change, but doesn't impact the freshness of the Tabasco? And here I thought I was actually making it last longer!

Do you refrigerate your Tabasco?