Obviously, the oil is going somewhere if you are topping up a full quart each month. My guess would be that a seal is bad and you are burning oil, just too slowly to see in the exhaust. This should be looked at by a competent mechanic.

In regard to your synthetic blend oil and your Lucas stabilizer, I would advise you to drop the stabilizer and switch to fully synthetic oil. The advantages of synthetic oil are these: One, it does not get as viscous (thick) in cold weather, which prevents oil from properly lubricating joints on a cold engine, causing the vast majority of engine wear. Two, it does not break down over time due to temperature changes and friction stress. In fact, if it wasn't for the additives in synthetic oil that break down and eventually need replacement, you would never need to change synthetic oil--only the oil filter. When you use a synthetic blend, you lose all of the benefits of synthetic oil, and you may as well just use straight conventional oil. Synthetic oil may cost more, but it is well worth the added expense. Plus, you can go for far longer between oil changes, so between that and the decreased engine wear, it pays for itself.

Sort of depends on whether you drive 250 miles a month, or 2500..

Agree that a quart every 1000 miles isn't critical - - - more often than that, there is a mechanical problem unless engine has lots of miles on it.

If the engine is not leaking you can assume the engine is burning the oil. If you have to add more that 1 quart per 1,000 miles, the piston rings are not controlling compression and cylinder wall splash from pressurized oil from between the connecting rods.

If the oil is burning in the engine it should turn the exhaust blue. If you dont see that it is probably just leaking.

check if the inside of the tail pipe is oily/greasy

I have a 2005 Hyundai Sonata with about 130k miles. I have to put a full quart of oil in the thing each month. I use part-synthetic oil with Lucas additive. It doesn't appear to be leaking; there aren't any spots under the car in the driveway. But I'm not sure if it's burning it off either since there isn't the notable smoke coming out of the tailpipe.

I just replaced the motor last year because it was doing the same thing an it eventually siezed. I really don't want to face that again. Any thoughts you have on the cause of this is greatly appreciated. Thanks!