New belts will stretch and need adjustment occasionally. General statement in my experience. If you can turn alternator fan with your finger the belt is too loose. (engine off needless to say) Another contributing factor is to check the pulleys for rust as car may have sat around too long before your purchase. Rust on grooves in pulleys will make the belt wear and loosen fast. Grooves that belt rides in should be almost shiney. If not you have to clean them up. Basically you have been describing a loose belt I believe.