The inside of the prop uses a hard, press fit rubber hub. The hub is the connection between the propeller shaft and the popeller. It's design is sacrificial in that if you ever hit the bottom, the hub would slip and sacrifice itself so you don't damage the rest of the drive, or it's gears or shafts. They spin if you hit something, and they also can spin if they are old props, as rubber does dry rot and shrink over time. Once they have spun, they will grab somewhat at lower rpms, and then let go when you really put the power down. And this is the slipping that you are feeling.
You can send the prop out to have it re-hubbed, but there is usually some down time with that. Most folks will buy a new prop so they can use the boat right away, and then send out their old prop, and keep it for a backup when they get it back in. If you don't know where the closest propeller repair shop is to you, simply call any dealer as all dealers work with propeller repair shops. This does not have to be a mercury dealer, you could call any dealer as a prop is not really brand specific. More than likely that dealer will offer to send the propeller out to be repaired for you. Figure on 1/2 the cost of a new propeller, roughly 75 to 100, to have a new hub installed into your propeller.
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