Hello : My Rogue now has 22K miles and the oil level on the dip stick has never moved. I have an old 66 Mustang and started using synthetic oil in it. The problem is synthetic is thinner than conventional oil. If you have any leaks they will be more pronounced with synthetic. I use a blend of 50/50 synthetic to conventional in the old car. As for your Rogue that's not driven much it sounds like it would be a candidate for synthetic since you probably reach the 3 months way before the 3K miles. Since synthetic doesn't break down you should be able to go more months between oil changes. You can call the companies that manufacture synthetic oil most have customer service lines listed on the bottle and get their opinion. Good luck with the oil level problem. Maybe a dye in the oil system that can be seen under ultra violet is in order, maybe a slow leak somewhere, drain plug or filter maybe ? Put a piece of clean cardboard under the car over night and check for stains in the morning.