TSA in the United States, and airport security in some other countries, will generally permit liquids in a secured, tamper evident bag (STEB) with a duty free receipt from within the past 24 hours, even if they are larger than the ordinary liquid size limit.
However, according to the TSA's website this officially only applies to liquids purchased internationally that are being brought into the US. Practically, you very well may have a decent shot of having it accepted in a sealed bag even if it's from a domestic source, but it would be a gamble. And even with a STEB, the TSA can reserve the right to refuse it, so there's always some risk when carrying liquids.
Many connections in the US are now possible without going through security again, so if this comes up, it's worth asking the airline if you could be rerouted elsewhere to avoid the need for rescreening, if there's an itinerary that's reasonable. Duty free often isn't a great deal in US airports anyway (you still have to pay sales tax).
You do have one other option besides discarding or checking it if you happen to be flying JetBlue and it's beer or wine: drink it. You can't serve yourself, but you can hand the bottle to the cabin crew, and they'll serve you. If the bottle is going to waste anyway, make friends on the flight.