We present the light curves of the 6.7 and 12.2 GHz methanol masers in the star-forming region G9.62+0.20E for a time-span of more than 2600d. The earlier reported period of 244 d is confirmed. The results of monitoring the 107 GHz methanol maser for two flares are also presented. The results show that flaring occurs in all three masing transitions. It is shown that the average flare profiles of the three masing transitions are similar. The 12.2 GHz masers are the most variable of the three masers with the largest relative amplitude having a value of 2.4. The flux densities for the different masing transitions are found to return to the same level during the low phase of the masers, suggesting that the source of the periodic flaring is situated outside the masing region, and that the physical conditions in the masing region are relatively stable. On the basis of the shape of the light curve we excluded stellar pulsations as the underlying mechanism for the periodicity. It is argued that a colliding wind binary can account for the observed periodicity and provide a mechanism to qualitatively explain periodicity in the seed photon flux and/or the pumping radiation field. It is also argued that the dust cooling time is too short to explain the decay time of about 100d of the maser flare. A further analysis has shown that for the intervals from days 48 to 66 and from days 67 to 135 the decay of the maser light curve can be interpreted as due to the recombination of a thermal hydrogen plasma with densities of approximately 1.6 × 106cm-3 and 6.0 × 105cm-3, respectively.