A very helpful response from customer support answered my question:
"The TS501 as well as all of our other TPMS tools can not hold or save the IDs for more than one set of wheels at a time. There would be no way to save the last set and this current set to do what it is you'd like to do. The tool does retain data from the last vehicle you worked on but not for the purposes outlined above.
"For OBD relearns the tool will require you to scan the sensors for the new set before plugging in to the car so it has the most up-to-date information available. This is usually done once the wheels are mounted on the vehicle, so the tool will write the correct positions to the computer. If it were to hold data from last years set or a set from several months ago and those wheels weren't mounted in the position the tool thinks they're in then the computer will have incorrect positional data which may be an issue on certain vehicles. It behooves us to enter the data anew every time for this reason."