Is your flow controller a variflow? Mine did this, so I bought a new battery. It turns out the old battery was fine, my Variflow just needed a really high charge. It would start off great in the morning and by early afternoon conk out unless I reduced the flow.
My other flow controller (cleaning warehouse) worked fine from the same battery.
Luckily enough I blew the Variflow by connecting the battery up wrong one morning, so wired my pressure switch back up, and now work without a flow controller, which I much MUCH prefer.
Because of my experience with the Variflow, I would never recommend one. Flog it on ebay and work without it!