Part of the issue is the offense, which has scored 4 runs or less in 15 of their last 22 games. The Cubs pen seemingly can't catch a break when every game they're needed to get 9+ outs in a close game. They're definitely a bad bullpen but one that could be minimized by winning a game 8-3 occasionally (or losing a game 8-3 I suppose, the Cubs don't do that a ton either). Instead every game is 3-1, 4-2, 4-3, 3-2, etc.
It was a similar issue last September when they were blowing all those games. Someone said earlier that it seems like the Cubs lead the league in games where multiple relievers are down because they've pitched too much and there's part of the reason why.