We study the effect of short-term variations of the evolution of AM CVn systems on their gravitational wave (GW) emissions and in particular Laser Interferometer Space Antenna (LISA) observations. We model the systems according to their equilibrium mass-transfer evolution as driven by GW emission and tidal interaction, and determine their reaction to a sudden perturbation of the system. This is inspired by the suggestion to explain the orbital period evolution of the ultra-compact binary systems V407 Vul and RX−J0806+1527 by non-equilibrium mass transfer. The characteristics of the emitted GW signal are deduced from a Taylor expansion of a Newtonian quadrupolar emission model, and the changes in signal structure as visible to the LISA mission are determined. We show that short-term variations can significantly change the higher order terms in the expansion, and thus lead to spurious (non-) detection of frequency derivatives. This may hamper the estimation of the parameters of the system, in particular their masses and distances. However, we find that overall detection is still secured as signals still can be described by general templates. We conclude that a better modelling of the effects of short-term variations is needed to prepare the community for astrophysical evaluations of real GW data of AM CVn systems.