Something is very wrong with this statement:
"Suddenly I now need to add an extra several gallons or the water never reaches the line even when you the pumps get turned back on. I just removed 3g and had to put 4 back in, which surely didn’t help my salinity."
This...isn't possible. It violates the laws of physics. If you take out 5 gallons of water, and you put back fresh salt water relatively soon (as in you haven't evaporated away days/gallons worth of water), then you'll need to put back 5 gallons of water.
Now as to what could be going on.
Here's a thought: in my aio, there's not a lot of room. Sometimes on it's own, or maybe because I was fiddling with it, or maybe because the pump is getting cruddy - sometimes, my return pump won't pump at full/normal speed. Either it's clogged up, or touching the wall and impeding flow. This type of thing will most definitely affect your water levels in the back chambers - which is where I suspect you have your ato sensors. Since the ATO maintains a water level, and not total gallons in the tank, this can lead to quite a bit of fluctuation in the total water in the system. You have to consider this type of action when doing water changes.
Further explanation - this is what happens in my tank: The pump has a habit of sucking against the wall and I don't notice the much reduced flow for a few days. This has the effect of "turning the pump off" which RAISES the water levels in the back chambers, and LOWERS the water level in the main display. Since it raises the level in the back chamber, the ATO stops adding top off water, and I've noticed 1/2 gallon or more of evaporation out of the tank. On a small AIO, that amount of water swings the salinity!
Now let's further play this out in some scenarios. Scenario 1: I could remove 5 gallons of water, replace it, but in the process jiggle my pump so that it starts pumping correctly again. The water level will drop significantly and I"m standing there going "I need to add more water than I took out." Which type of water do I add? If I add more salt water - I'll raise the salinity. If I add fresh water, I'll lower the salinity. I'm screwed because I removed saltwater that WASN'T at 35ppm or 1.026. Get it? If I repeated this process every week, I'll move my salinity quite a bit in a short amount of time. EZ to do on a nano tank - and a mistake I've made myself.
So scenario 2 - the RIGHT way to do it: Check your equipment before you take any water out! You can't tell if everything is good by just looking at the water level - the ATO will maintain that level no matter what - but there could still be more or less water in your system overall! In my case, I make sure the pump is pumping correctly, if it was obstructed, the water level in the back will drop once it gets moving again, the ATO will top it off with fresh water, and I wait a while to do any water changes to let the salinity swing settle down. EVEN BETTER is to check the salinity of the water you're taking out first. If it's elevated or low, you should address that problem first. THEN you do the water change, and physics says you'll need to add in the exact same amount you took out. If you mixed your salt correctly, and your salinity meter/refractometer/whatever is working, then everything will be ducky!
One last note: sometimes you have to fiddle with your ato sensor. If you move it up or down, that'll affect your salinity in a small tank (because it'll either add a bunch of fresh water lowering overall salinity, or it won't - raising overall salinity). If you're fiddling with things - then it's best to measure your salinty, get it correct in the tank and get your water levels correct - then put your sensor right at the water level.
The only other things I can think of are 1) is your salinity checking device working? 2) is your calibration fluid good? 3) are you sure? Have you checked it against something else? 4) are you removing water at an excessive rate - like you don't have a skimmer that's overflowing and you empty it 5 times a day right? 5) are you dosing anything? Some things that you dose raise salinity and you'll need to correct for that. On a nano tank all for reef is nice because you don't need to dose a lot, and the high cost is palatable and it won't swing your salinity.
So ya - something like that is going on. My money is on your water levels in the back chamber are fluctuating, which is swinging your salinity due to ATO action, and you're removing water that isn't at 35ppm. Since your salinity is going UP, I'd suspect you're adding back in more saltwater which will have the effect of raising your salinity over time.
Hope this helps.