Andy, here's something else which might help to "bring it back" more quickly:
Even though it is showing "out of range", feed it a calibration figure anyway. For me, this action seems to nearly always provoke recovery at the next 5-minute readout mark. I might be imagining things... but without that finger-poke entry, it seems to miss a lot more data points before realizing that the Sensor and Transmitter have been brought back in range.
But the other BIG trick which I use to make this recovery happen is to sit down at the sofa when I enter the finger-poke reading- with the CHARGER PLUGGED IN. That's probably the real reason behind my "very-next-time" recoveries.
AFAICT, the battery voltage seems to be proportional to a lot of the electrical behavior in the Receiver: For example, the alarm buzzer seems louder when it's actually plugged in. If the VRMs in the radio section are simple proportional circuits (rather than more complicated "regulated power supply" circuits), as I suspect they are... then you can provide more power to the radio by actually plugging it in.
The DC voltage which comes from the charger is quite a bit HIGHER than the maximum voltage which the Receiver's battery will put out while discharging. (That is, whenever it's being used as the power source WITHOUT extra "boost" from the charger.) So, even when the Receiver shows a charge state of "3 bars", you're getting much less voltage from the battery terminals. When the charger is plugged in, of course, the terminals differ by the charger voltage-- a higher figure.
If it exists, then this "extra" radio power at the Receiver end helps in both directions-- it transmits a slightly stronger "Wake up and tell me your reading!" signal to your old, weakened Transmitter, and it helps the Receiver hear the weakened reply.
Plug it in, feed it an extra calibration, and see if that helps.
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All other comments are A+, and I agree. Transmitter age is critical, because the battery gets used up. Receiver age is critical, because the battery "wears out" after it's been charged/discharged to many times. And Richard157 is right on the money about Receiver distance-- if the signal path goes through your body tissue, the signal gets reduced 10-20x as much as it gets reduced while spreading out and getting scattered in the same distance of air.