I'm not sure if this is modeled into R3E, but it may be due to dirty air. When you're trailing a car, especially closely, you are in the "wake" of that car which means there isn't as much air pushing on the front of your car which means you have less braking ability. Plus, the draft/slipstream will be pulling you forward which also can make your brakes less effective.
A general tip, especially when you start racing online, is to anticipate when the lead driver will brake and brake a few meters before that. It's much more important to have better exit speed than entry speed, so brake a little early, follow him/her through the turn and focus on getting a better exit so you can get a run on them after the turn. Chances are the lead driver is watching you in the mirror and feeling a bit of pressure or worrying about how close you're going to get to them. As a result they may not take a perfect approach to the turn and their exit speed may suffer, so by focusing on getting your best exit speed possible you'll be set up to get past them as you exit. Don't worry about braking at the very latest point, there have been many times where I braked rather early but got such a good exit that I was able to make the pass or at least gain some good ground.
When you finally go online, remember this mantra: Don't force the overtake, force a mistake. Hang right on their bumper, stick your nose left, stick your nose right (without actually getting alongside them), keep them guessing as to what you're going to do, they'll be so focused on worrying about you that eventually they will likely slip up and you'll be able to cruise right on by knowing you made a clean pass.
Watch this video to learn about why exit speed is so important, and many other tidbits about how to drive faster. It's a bit long, and old, but still totally relevant and accurate.
