If it's not dripping, then it's burning.

If it's burning, it's usually by getting around the piston rings (gaskets around the pistons which form a seal between the piston and the cylinder wall). The rings get worn or dry out with age, and oil (which is squirted through the piston behind the ring - meaning on the non-combustion side of the ring) gets past the ring into the combustion chamber and burns up with your fuel. There are some other ways oil can get pulled out of where it is supposed to stay and end up in the cylinder, but I don't know much about that. Maybe someone else can chime in.

Unfortunately, the piston rings are at the very heart of the engine and take hours and hours of disassembly work to replace - it's far cheaper to just add oil. Some motor oil manufacturers offer types of oil that are supposed to soften old rings and help them form a better seal, reducing oil loss, but I don't know if those products work as well as their labels claim.

Although most people think Jiffy Lube should be avoided like the gates of hell, I've had pretty good experiences with getting my oil changed at Valvoline and Firestone, and I know Valvoline offers free top-offs, so if you pass one regularly, it can be fairly easy to drive through once or twice between changes and have them top you off. I did that in my old Prelude, which was burning about quart every 1000 miles after it got over 125k miles. Stopping there for a top-off was super-convenient - I didn't even get out of my car or sign a receipt! Just pull in, pop the hood, get a top off, and go.