I’m not on Solo, I use Performer, but I think the functionality is the same. Even if you don’t save the song, the Song Input and Output gains will revert to the last setting, if the State behavior is not set to save. Here’s how you check that…
If you click on the text of one of them, i.e. Input gain, then select “STATES” here on the top left
If I had Input Gain checked here, then when I save that song the input gain will be recalled to whatever you saved. But since it’s unchecked, that means it won’t recall the gain setting, and will revert to the last setting. Think of it as being an “Active Fader” that’s always active. You probably don’t have it checked which is why you’re getting that behavior. But note that if it’s checked, IIRC each Song state needs to be saved. The State behavior refers to Song states. So when checked, you could actually have the Output gain change for each state. Which is why I leave it unchecked.
FWIW I leave mine unchecked, and I try to have all songs run at 0 db output or input, for consistency. Yes, there are a couple complex songs where, after several tweaking sessions, it was far easier to just change the Song output, but I try to avoid that. Doesn’t mean it’s wrong to do it, whatever works for you is all good.