The recommended load for both the high and low output versions of the Sonata is 47K. Assuming your loading is in that vicinity, the amount of current flowing through the phono cable under typical music conditions would be in the rough ballpark of one-tenth of one-millionth of an ampere for the high output version of the cartridge, and one-hundredth of one-millionth of an ampere for the low output version.
Given that, I can't see how loss of breakin, if any, would be affected by frequency of use.
The only hypotheses I can envision are the two described below. Although they may seem somewhat improbable, I would think that their likelihood is considerably greater than the likelihood of a tiny fraction of a millionth of an amp making a difference:
1)The month of non-use perhaps caused the cartridge suspension to tighten up slightly, and during the course of your initial listening session following the month of non-use, during which you concluded that the cable had lost its breakin, the suspension gradually loosened up and regained its normal compliance. That perhaps being the reason for the improved sonics when you re-tried the cable following the burn-in process you subjected it to. Or,
2)Perhaps in phono applications the cable tends to lose its breakin over time regardless of how frequently or infrequently records are played, and it was a coincidence that the loss of breakin happened to become apparent following the month of non-use.