After a good long warm up period, if the scale is still losing zero too fast, you should try using a fresh battery instead of the transformer. If that doesn't work then the scale needs service.
I have a voltmeter here on my desk (on a UPS box), and during the summer months it's not unusual to see the line voltage vary from 109 to 122 VAC (it's 116 VAC right now), and sometimes it shifts very fast, not a slow drift up or down. That may be what's happening in your case. Generally, electronics have good voltage regulation circuits, but a scale is so sensitive that it may not be able to keep up.