Beer Reduction Sauce - Refrigerate or Not?

Hello from Juneau, Alaska USA. From time to time, I’ve been bottling tiny quantities of a home made reduction that I just call ‘Alaskan Awesome Sauce’, which consists of Alaskan Amber, balsamic, brown sugar and a few other things depending on what is on hand.  While it reduces for several hours and I end up with a syrupy and incredibly delicious (halibut, salmon, chops, steak…) reduction, I store it in a glass bottle with a ceramic top and rubber gasket so its pretty airtight but, should this stuff always be refrigerated?  It all gets consumed pretty quickly so shelf-life isn’t a concern really.  If I refrigerate, it definitely becomes more syrupy/thicker and it also seems to separate a bit, with some of the sugars settling to the top.  The color is a gorgeous purple/red.  Ideas?

Thank you!

Mark

I’m going to guess with the balsamic that the sauce can be kept on the shelf safely like ketchup as the pH will be below 4.5. (Ketchup does say to refrigerate but that is for freshness.)  There is still the possibility of spoilage that ruins the flavor of the sauce without being dangerous.

Doesn’t seem like it could hurt to refrigerate.