The week ends are known to be pretty bad. People have time to play so most will be online. If they have other plans for the week end, they'll get a 3d peace treaty for instance. So overall, this will decrease the number of potential targets. I personally take long PT on week ends when it's not in cooldown. Because I know I won't find opponents for the amount of time I can play. And if others think like me, then everyone will be on paid PT and they'll be no one left to attack. So a vicious circle that feeds the no opponent situation.
The other scenario is a lot of people quit playing and getting hammered to a medal range where they can't be attacked by top players anymore. And new players can't catch up with the old timers and find a way to move up the medal range. If someone starts an account right now, it'll take them a long time to replace an old timer that has quit playing (7 months lag). The problem will be how to replace older player accounts. As it evolves, you'll have a small group of 200 players going over 3000 medals, while the majority sits around 1000 medals and below and a very small number lies between 1000 and 3000.
If they don't change the matchmaking and allow a larger reach for top players (see my reply to Tim's medal post), the top 200 players will be playing in a silo and can only attack each other when one of them logs off. And that's not a lot of potential opponents for everyone in that silo.