Check the cables are OK, (the outer cable to the rear mech has a habit of corroding inside*), and if they're ok re-index the gears and see how you go.
This is a great vid that de-mystifies setting up gears, it's well worth a watch.
*during routine maintenace I put a dab of grease on the ends of this short outer cable to help stop water ingress, and TBH I've not had any issues since I started doing it either
[EDIT] x posted with fossy, must type faster
Shouldn't be as you say, but I managed to cabbage one really quickly once on a brand new bike. It got wet on one of it's first rides out and a week or so later the gear change was pants. I had to put a new short piece of outer cable to the rear mech to fix it.