Future communication networks are expected to connect massive distributed artificial intelligence (AI). Exploiting aligned priori knowledge of AI pairs, it is promising to convert high-dimensional data transmission into highly-compressed semantic communications (SC). However, to accommodate the local data distribution and user preferences, AIs generally adapt to different domains, which fundamentally distorts the SC alignment. In this paper, we propose a zero-forget domain adaptation (ZFDA) framework to preserve SC alignment. To prevent the DA from changing substantial neural parameters of AI, we design sparse additive modifications (SAM) to the parameters, which can be efficiently stored and switched-off to restore the SC alignment. To optimize the SAM, we decouple it into tractable continuous variables and a binary mask, and then handle the binary mask by a score-based optimization. Experimental evaluations on a SC system for image transmissions validate that the proposed framework perfectly preserves the SC alignment with almost no loss of DA performance, even improved in some cases, at a cost of less than 1% of additional memory.