Resending old frame when a damaged frame has been received in one bit sliding window protocol
Shouldn't it be the case that client A now sends a frame with the sequence number inverted, new data but the acknowledgement is not inverted?


This could indeed be done when the error occured in the data. i.e. you're sure that it wasn't the acknowledgement or sequence number that was damaged. In that case, sender A could indeed send a new frame as described and avoid sending unnecessary duplicates.

However, although an error can be detected, it can not be detected where the error occured (in the data, acknowledgement or sequence number). If the error occured in the aknowledgement number then the client may unrightfully think that his previously sent frame was received correctly while it actually wasn't received correctly and so, if he sents a new frame with new data as proposed in the question, a client will miss a frame!