Poké Balls

It's you.

Catch mechanics are understood. It stops getting harder once you hit level 30, since wild pokemon levels are capped at 30. See the page on catch mechanics, there's a great description of how catching works: https://pokemongo.gamepress.gg/catch-mechanics

Higher level players are more used to throwing good curve balls... which mathematically is even better than using a razzberry.

You are probably just finding more higher level Rats/Pidgeys.

I look at the CP before throwing balls. What CP is going to be a tough catch is species specific. High level fast evolvers are all usually a multi-ball fight. Squirtles, Bulbasaurs, Charmanders, Pikachus are all ball thieves. Great and ultra balls seem to help most of the time, but some pokies just seem determined not to be caught. Unless it is one I really want, I usually move on after two or three balls.

Ive noticed this as well and so has my GF who is now level 31. It was harder I believe before when we did not have species specific catch bonus badges.
If you have not already you will need to master the curved great throw. I recommend trying to master the nice first before going to great. IMO people try to go for excellent which is a bad idea. I try to aim for the circle right when it shrinks from nice to great. By not throwing great curves you will increase the time you need to spend gathering resources so this is essential skill for improving game play besides the fact you will catch more and have a lower flee rate.