When I brought my 2005 transit, I had the same issues. Took it back to the garage and they changed the filter and said it was draining back. Got it back and still had the same issue. Mine would struggle to start in a morning but once warm was ok for a while but gradually got worse.
I spoke to a Ford technician who knew straight away what it was. He said it was the timing belt/chain.
He replaced it but also had to change the cover too. This cured it and been good since.