Sure I can shed some light on this. You're probably running into champions that are reducing your team's turn meter while increasing their own. Deacon Armstrong and Lyssandra are two really common examples since they do both Increase and Decrease. This means you're not getting turns and they are getting more turns. Especially with Lyssandra since she can also completely wipe out a single champion's turn meter after doing the aoe Increase/Decrease. 

The short answer is: they're faster than you. The equation for calculating turns is surprisingly complex, but the jist of it is - the faster you are, the more turns you get, and the more likely it is that you get a turn before they do, even if they "look" like they're going to be next. Couple that with abilities to reduce your turn meter and increase theirs, and it's very possible for them to get a ton of turns before you - especially if you are slow.