I think you'll find that problem with any analog tuner, not just a tubed one.
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Older tuners can be subject to drift as components in the local oscillator can become temperature sensitive over time (decades).
It is normal for some drift to be present even in a solid state tuner. Back in the tube days, a circuit called AFC (automatic frequency control) was developed that is supposed to prevent drift in either a tube or solid state tuner. If you encounter drift in such a tuner, the discriminator (FM demodulation) transformer is out of alignment.