Radiocarbon dating range
This isn't a fundamental limit as more accurate measurements could go further back, but at some point you'd simply run out of C-14 atoms.
With our current kit 40-50K years is about the limit.
Carbon-14 makes up about 1 part per trillion of the carbon atoms around us, and this proportion remains roughly constant due to continual production of carbon-14 from cosmic rays.
The Radiocarbon Revolution Since its development by Willard Libby in the 1940s, radiocarbon (14C) dating has become one of the most essential tools in archaeology.
Radiocarbon dating was the first chronometric technique widely available to archaeologists and was especially useful because it allowed researchers to directly date the panoply of organic remains often found in archaeological sites including artifacts made from bone, shell, wood, and other carbon based materials.
Compared to conventional radiocarbon techniques such as Libby's solid carbon counting, the gas counting method popular in the mid-1950s, or liquid scintillation (LS) counting, AMS permitted the dating of much smaller sized samples with even greater precision.
Regardless of the particular 14C technique used, the value of this tool for archaeology has clearly been appreciated.