At first I felt it had something to do with fixture congestion - Premier League doesn't give two fucks about Champions League when it's putting together the fixture schedule - but I don't think that's it. Look at Juventus's fixtures during September, for instance:
Wed 30th September
CL Juventus 19:45 SevillaSat 26th September
SER A Napoli 2 1 Juventus FTWed 23rd September
SER A Juventus 1 1 Frosinone FTSun 20th September
SER A Genoa 0 2 Juventus FTTue 15th September
CL Manchester City 1 2 Juventus FTSat 12th September
SER A Juventus 1 1 Chievo FT
6 games in 2 weeks. That's literally a game every 3rd day. And all of them are vital. No league cup to lighten things up. The same thing is true for Leverkusen and other Bundesliga clubs:
Tue 29th September
CL Barcelona 2 1 Bayer Leverkusen FTSat 26th September
BUN Werder Bremen 0 3 Bayer Leverkusen FTWed 23rd September
BUN Bayer Leverkusen 1 0 Mainz FTSun 20th September
BUN Borussia Dortmund 3 0 Bayer Leverkusen FTWed 16th September
CL Bayer Leverkusen 4 1 BATE Borisov FTSat 12th September
BUN Bayer Leverkusen 0 1 SV Darmstadt 98 FT
Here's Barca's fixture schedule for the same period:
Tue 29th September
CL Barcelona 2 1 Bayer Leverkusen FTSat 26th September
LIGA Barcelona 2 1 Las Palmas FTWed 23rd September
LIGA Celta Vigo 4 1 Barcelona FTSun 20th September
LIGA Barcelona 4 1 Levante FTWed 16th September
CL Roma 1 1 Barcelona FTSat 12th September
LIGA Atletico Madrid 1 2 Barcelona FT
On the face of it there's very little excuse for the weak start of the Premier League clubs. Bad luck? Coincidence? Maybe. Maybe even probable. This year's start to Champions League has certainly been a one off. But the weak start is not why Premier League is running the very real risk of losing the coefficient at the moment. It's because English clubs have systematically underperformed for a while now. Why exactly is that?
You can certainly make the argument that English clubs aren't as good as Bayern or the two Spanish giants, but you can't convince me that Chelsea (on last year's form) is a worse club than Atletico Madrid or Juventus or Dortmund. I watch all of them regularly enough to know that's not true. So what is it? Fixture congestion post Christmas where PL automatically takes precedence? Lack of a winter break? Is the extra domestic cup putting extra strain on the teams? Do English players, on average, suffer more injuries than their peers abroad, which means English clubs can field a full team in the knockout rounds less often?