I had the same issue with mu ATU-1000. While tuning fine with a single tone, it was retuning constantly on the lower part of 40M band and ONLY on LSB. When I switched to USB there was no issue. This prompted me to do an impedance sweep in this part and while resistance was well within range of the ATU, reactance was looking like a steep hill, rising as frequency was going down. When transmitting in LSB the SWR actually rose with my voice and the ATU-1000 was kicked into retuning, and my TRX into ALC power reduction. I thought there was something wrong with my radio, than with the ATU, but after the impedance sweep of the antenna, I realized it was tad short and below 7.110 SWR rose steeply from increasing reactivity. I lengthened the antenna a bit and now all is fine.