Does the modem or transceiver show any alarms ?
Some guesses: TX LO PLL synth fault, overheating due to fan failure, power supply problems.
The P300 modem manual is here:https://www.ironlinkus.com/ironlink/manuals/docs/Modems/Paradise/P3x0h.pdf
(3.5 Mbytes pdf file)
The Anacom manual is here https://www.anacominc.com/Anasat_Ku_Band_Rev4.pdf
(3.8 Mbytes pdf file) and it shows how to access status information for the TX Offset and TX synth oscillators, also the power supply voltages are shown.
If you are getting exact jumps of 0, 8kHz, 12 kHz I would suspect a PLL fault in the modem as that is intended to work with small frequency steps. The Anacom goes in large 1 MHz steps.
Note that the Anacom unit uses single 10 MHz crystal reference so it would be worth checking the receive frequency also.
For a PLL fault, a possible workaround would be to try changing the Anacom by 1 MHz (or 2 MHz or 3 MHz etc) and the modem an equal amount the other way. That way you may get to use different pins on the PLL chips and might, with luck, avoid a dry joint. With patience you can try tuning to a number of frequencies and looking to see if any are missing or not as commanded.
It is temperature related?
Does cycling the power on the modem fix the problem?
Does cycling the power on the Anacom fix the problem?
Try to isolate which part is causing the fault. While you have this symptom, tell the satellite operator and look at the whole output spectrum at the Anacom output in case the synthesisers are generating a spurious carrier and interfering with another service on the satellite.
It is very embarassing if when you type some specific digit in the frequency number it makes a wrong frequency carrier appear spaced well away across the band !
Best regards, Eric.