Every theremin oscillator has a little thermal drift, especially after powering it on until all components are on working temperature. While a slow drift of 0.1% over a few minutes is tolerable in many RF applications, a theremin oscillator running at 500kHz and drifting by 500Hz makes the instrument unplayable. That’s why many thereminists pre-heat their instruments by switching them on about 15 to 30 minutes before playing depending on the instrument, because once the thermal working point (balance between heating up through power dissipation and ambient temperature) reached, the drift is reduced by several orders of magnitude. Calibrated or tuned after warming up, the field will remain much more stable. This applies to the open.theremin v3 and v4 (where the RF circuit parts are nearly identical, so no major difference to expect), but also to the Moog Etherwave Standard and Plus Theremins, and even the famous Russian tVox tour.
While in most other RF circuits, additional things can be done to stabilize oscillators, using PLL techniques, Xtal references or just simple AFC circuits, all this can not be used in classic heterodyning theremins because the principle of operation requires that the oscillator frequencies are easily bendable by very small capacitance changes. The advantage of the heterodyning principle is that the effect of oscillator drift can be reduced by having the oscillators drifting but in a coupled way, so that both might drift up or down together, by keeping always the same difference (heterodyning) frequencies. You can find such designs in professional instruments like the Etherwave Pro, but it should be understood that it has a more than 20 times higher price tag than an open.theremin.
With the ~130€ for a readily built OTv4, you get a similar playability and functionality as with a 550€ Moog Etherwave Plus theremin and you are above the 300€ Moog Theremini. So, be happy with what you have built at an advantageous price and give it the required 15 to 20 minutes to warm up before calibrating it as you would also have to do with more expensive instruments.
BTW: My main instrument wich I use for daily practicing and for teaching is always set up and powered on in my music room, so that whenever I want to play, I need just to power the amplifier and do fine tune it by one or two mm with the pitch and volume knobs. That saves time! ;-)
